From 06398c4baf788ca95dc568267226532995aae7d9 Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Wed, 19 Jun 2013 01:49:50 +0530 Subject: [PATCH 01/33] Added a 3 link pendulum problem, with massless links. and Added a 3 link pendulum problem, with links as RigidBodies --- three_link_pendulum/three_link_pendulum.py | 141 ++++++++++++++++++ .../three_link_pendulum_massless_links.py | 90 +++++++++++ 2 files changed, 231 insertions(+) create mode 100644 three_link_pendulum/three_link_pendulum.py create mode 100644 three_link_pendulum/three_link_pendulum_massless_links.py diff --git a/three_link_pendulum/three_link_pendulum.py b/three_link_pendulum/three_link_pendulum.py new file mode 100644 index 0000000..11eed83 --- /dev/null +++ b/three_link_pendulum/three_link_pendulum.py @@ -0,0 +1,141 @@ +#For this one we assume massless links +from sympy import symbols,sympify +from sympy.physics.mechanics import * + +#Number of links = 3 +N_links = 3 + +#Number of masses = 3 +N_bobs = 3 + +#Defining Dynamic Symbols ................ + +#Generalized coordinates ... +q = dynamicsymbols('q:' + str(N_bobs)) + +#Generalized speeds ... +u = dynamicsymbols('u:' + str(N_links + 1)) + +#Mass of each bob: +m = symbols('m:'+str(N_bobs)) + + +#Length and mass of each link .. +l = symbols('l:' + str(N_links)) +M = symbols('M:' + str(N_links)) +#For storingInertia for each bob : +i = symbols('i:'+str(N_bobs)) + + +#gravity and time .... +g, t = symbols('g t') + + +#Now defining an Inertial ReferenceFrame First .... + +I = ReferenceFrame('I') + +#Getting more referenceframes for RigidBodies ... + +A = I.orientnew('A', 'Axis', [q[0], I.z]) +B = I.orientnew('B', 'Axis', [q[1], I.z]) +C = I.orientnew('C', 'Axis', [q[2], I.z]) + +#Setting angular velocities of new frames ... +A.set_ang_vel(I, u[0] * I.z) +B.set_ang_vel(I, u[1] * I.z) +C.set_ang_vel(I, u[2] * I.z) + + + +# An Origin point, with velocity = 0 +O = Point('O') +O.set_vel(I,0) + +#Three more points, for masses .. +P1 = O.locatenew('P1', l[0] * A.y) +P2 = O.locatenew('P2', l[1] * B.y) +P3 = O.locatenew('P3', l[2] * C.y) + +#Setting velocities of points with v2pt theory ... +P1.v2pt_theory(O, I, A) +P2.v2pt_theory(P1, I, B) +P3.v2pt_theory(P2, I, C) +points = [P1,P2,P3] + +Pa1 = Particle('Pa1', points[0], m[0]) +Pa2 = Particle('Pa2', points[1], m[1]) +Pa3 = Particle('Pa3', points[2], m[2]) +particles = [Pa1,Pa2,Pa3] + + + +#defining points for links(RigidBodies) +#Assuming CoM as l/2 ... +P_link1 = O.locatenew('P_link1', l[0]/2 * A.y) +P_link2 = O.locatenew('P_link1', l[1]/2 * B.y) +P_link3 = O.locatenew('P_link1', l[2]/2 * C.y) +#setting velocities of these points with v2pt theory ... +P_link1.v2pt_theory(O, I, A) +P_link2.v2pt_theory(P_link1, I, B) +P_link3.v2pt_theory(P_link2, I, C) + +points_rigid_body = [P_link1,P_link2,P_link3] + + +#defining inertia tensors for links +#Since links are rods, rotating axis= z-axis +#Hence, xx = yy = (1/12)*m*l**2 + +i0 = (1.0/12)*M[0]*l[0]**2 +i1 = (1.0/12)*M[1]*l[1]**2 +i2 = (1.0/12)*M[2]*l[2]**2 + +inertia_link1 = inertia(A,i0,i0,0) +inertia_link2 = inertia(B,i1,i1,0) +inertia_link3 = inertia(C,i2,i2,0) + +#Defining links as Rigid bodies ... + +link1 = RigidBody('link1', P_link1, A, M[0], (inertia_link1, O)) +link2 = RigidBody('link2', P_link2, B, M[1], (inertia_link2, P1)) +link3 = RigidBody('link3', P_link3, C, M[2], (inertia_link3, P2)) +links = [link1,link2,link3] + + +#Applying forces on all particles , and adding all forces in a list.. +forces = [] +for particle in particles: + + mass = particle.get_mass() + point = particle.get_point() + forces.append((point, -mass * g * I.y) ) + +#Applying forces on rigidbodies .. +for link in links: + mass = link.get_mass() + point = link.get_masscenter() + forces.append((point, -mass * g * I.y) ) +kinetic_differentials = [] +for i in range(0,N_bobs): + kinetic_differentials.append(q[i].diff(t) - u[i]) + +#Adding particles and links in the same system ... +total_system = [] +for particle in particles: + total_system.append(particle) + +for link in links: + total_system.append(link) + +kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinetic_differentials) +fr, frstar = kane.kanes_equations(forces, total_system) + +print fr + + + + + + + diff --git a/three_link_pendulum/three_link_pendulum_massless_links.py b/three_link_pendulum/three_link_pendulum_massless_links.py new file mode 100644 index 0000000..8b7561e --- /dev/null +++ b/three_link_pendulum/three_link_pendulum_massless_links.py @@ -0,0 +1,90 @@ +#For this one we assume massless links +from sympy import symbols +from sympy.physics.mechanics import * + +#Number of masses = 3 +N_bobs = 3 + +#Defining Dynamic Symbols ................ + +#Generalized coordinates ... +q = dynamicsymbols('q:' + str(N_bobs)) + +#Generalized speeds ... +u = dynamicsymbols('u:' + str(N_links + 1)) + +#Mass of each bob: +m = symbols('m:'+str(N_bobs)) + +#Length of each link .. +l = symbols('l:' + str(N_links)) + + +#gravity and time .... +g, t = symbols('g t') + + +#Now defining an Inertial ReferenceFrame First .... + +I = ReferenceFrame('I') + +#Getting more referenceframes for RigidBodies ... + +A = I.orientnew('A', 'Axis', [q[0], I.z]) +B = I.orientnew('B', 'Axis', [q[1], I.z]) +C = I.orientnew('C', 'Axis', [q[2], I.z]) + +#Setting angular velocities of new frames ... +A.set_ang_vel(I, u[0] * I.z) +B.set_ang_vel(I, u[1] * I.z) +C.set_ang_vel(I, u[2] * I.z) + + + +# An Origin point, with velocity = 0 +O = Point('O') +O.set_vel(I,0) + +#Three more points, for particles .. +P1 = O.locatenew('P1', l[0] * A.x) +P2 = O.locatenew('P2', l[1] * B.x) +P3 = O.locatenew('P3', l[2] * C.x) + +#Setting velocities of points with v2pt theory ... +P1.v2pt_theory(O, I, A) +P2.v2pt_theory(P1, I, B) +P3.v2pt_theory(P2, I, C) +points = [P1,P2,P3] + +#Defining particles ... +Pa1 = Particle('Pa1', points[0], m[0]) +Pa2 = Particle('Pa2', points[1], m[1]) +Pa3 = Particle('Pa3', points[2], m[2]) +particles = [Pa1,Pa2,Pa3] + + + +#Applying forces on all particles , and adding all forces in a list.. +forces = [] +for particle in particles: + + mass = particle.get_mass() + point = particle.get_point() + forces.append((point, -mass * g * I.y) ) + + + + +print forces +kinetic_differentials = [] +for i in range(0,N_bobs): + kinetic_differentials.append(q[i].diff(t) - u[i]) + +print kinetic_differentials + +kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinetic_differentials) +fr, frstar = kane.kanes_equations(forces, particles) + +print(fr+frstar) + + From 11a0059c78f0064a33ae1c2fdca061a920e80360 Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Wed, 19 Jun 2013 01:53:00 +0530 Subject: [PATCH 02/33] Added README Changed inertia value --- three_link_pendulum/README | 4 ++++ three_link_pendulum/three_link_pendulum.py | 6 +++--- 2 files changed, 7 insertions(+), 3 deletions(-) create mode 100644 three_link_pendulum/README diff --git a/three_link_pendulum/README b/three_link_pendulum/README new file mode 100644 index 0000000..9f6552e --- /dev/null +++ b/three_link_pendulum/README @@ -0,0 +1,4 @@ +This is a 3 link pendulum problem, +it includes two scripts, one for massless links, +and other assuming links as RigidBodies .. +I will add a fig soon .. diff --git a/three_link_pendulum/three_link_pendulum.py b/three_link_pendulum/three_link_pendulum.py index 11eed83..b0e99d5 100644 --- a/three_link_pendulum/three_link_pendulum.py +++ b/three_link_pendulum/three_link_pendulum.py @@ -87,9 +87,9 @@ #Since links are rods, rotating axis= z-axis #Hence, xx = yy = (1/12)*m*l**2 -i0 = (1.0/12)*M[0]*l[0]**2 -i1 = (1.0/12)*M[1]*l[1]**2 -i2 = (1.0/12)*M[2]*l[2]**2 +i0 = (1.0/3)*M[0]*l[0]**2 +i1 = (1.0/3)*M[1]*l[1]**2 +i2 = (1.0/3)*M[2]*l[2]**2 inertia_link1 = inertia(A,i0,i0,0) inertia_link2 = inertia(B,i1,i1,0) From d5f2d44d1cdfad02031ebaa125dab82275908b75 Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Wed, 19 Jun 2013 01:58:30 +0530 Subject: [PATCH 03/33] Update three_link_pendulum.py --- three_link_pendulum/three_link_pendulum.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/three_link_pendulum/three_link_pendulum.py b/three_link_pendulum/three_link_pendulum.py index b0e99d5..8cd7f9a 100644 --- a/three_link_pendulum/three_link_pendulum.py +++ b/three_link_pendulum/three_link_pendulum.py @@ -1,4 +1,4 @@ -#For this one we assume massless links +#For this one we assume RigidBody links from sympy import symbols,sympify from sympy.physics.mechanics import * From a61e6028d6c8e470a5548cc7ec5ed618e493109b Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Wed, 19 Jun 2013 23:24:11 +0530 Subject: [PATCH 04/33] Modified script for two dimensional joints --- three_link_pendulum/README | 4 +- three_link_pendulum/three_link_pendulum.py | 66 ++++++++------ .../three_link_pendulum_massless_links.py | 90 ------------------- 3 files changed, 42 insertions(+), 118 deletions(-) delete mode 100644 three_link_pendulum/three_link_pendulum_massless_links.py diff --git a/three_link_pendulum/README b/three_link_pendulum/README index 9f6552e..e07eeb0 100644 --- a/three_link_pendulum/README +++ b/three_link_pendulum/README @@ -1,4 +1,2 @@ -This is a 3 link pendulum problem, -it includes two scripts, one for massless links, -and other assuming links as RigidBodies .. +This is a 3 link pendulum problem, assuming links as RigidBodies .. I will add a fig soon .. diff --git a/three_link_pendulum/three_link_pendulum.py b/three_link_pendulum/three_link_pendulum.py index b0e99d5..c5ec0aa 100644 --- a/three_link_pendulum/three_link_pendulum.py +++ b/three_link_pendulum/three_link_pendulum.py @@ -1,4 +1,4 @@ -#For this one we assume massless links +#For this one we assume RigidBody links from sympy import symbols,sympify from sympy.physics.mechanics import * @@ -10,11 +10,14 @@ #Defining Dynamic Symbols ................ -#Generalized coordinates ... -q = dynamicsymbols('q:' + str(N_bobs)) +#Generalized coordinates(angular) ... -#Generalized speeds ... -u = dynamicsymbols('u:' + str(N_links + 1)) +alpha = dynamicsymbols('alpha1 alpha2 alpha3') +beta = dynamicsymbols('beta1 beta2 beta3') + +#Generalized speeds(angular) ... +alphad = dynamicsymbols('alpha1 alpha2 alpha3',1) +betad = dynamicsymbols('beta1 beta2 beta3',1) #Mass of each bob: m = symbols('m:'+str(N_bobs)) @@ -23,9 +26,9 @@ #Length and mass of each link .. l = symbols('l:' + str(N_links)) M = symbols('M:' + str(N_links)) -#For storingInertia for each bob : -i = symbols('i:'+str(N_bobs)) - +#For storing Inertia for each link : +Ixx = symbols('Ixx:'+str(N_links)) +Iyy = symbols('Iyy:'+str(N_links)) #gravity and time .... g, t = symbols('g t') @@ -35,16 +38,20 @@ I = ReferenceFrame('I') -#Getting more referenceframes for RigidBodies ... +#And some other frames ... + +A = ReferenceFrame('A') +A.orient(I,'Body',[alpha[0],beta[0],0],'ZXY') +B = ReferenceFrame('B') +B.orient(I,'Body',[alpha[1],beta[1],0],'ZXY') +C = ReferenceFrame('C') +C.orient(I,'Body',[alpha[2],beta[2],0],'ZXY') -A = I.orientnew('A', 'Axis', [q[0], I.z]) -B = I.orientnew('B', 'Axis', [q[1], I.z]) -C = I.orientnew('C', 'Axis', [q[2], I.z]) #Setting angular velocities of new frames ... -A.set_ang_vel(I, u[0] * I.z) -B.set_ang_vel(I, u[1] * I.z) -C.set_ang_vel(I, u[2] * I.z) +A.set_ang_vel(I, alphad[0] * I.z + betad[0] * I.x) +B.set_ang_vel(I, alphad[1] * I.z + betad[1] * I.x) +C.set_ang_vel(I, alphad[2] * I.z + betad[2] * I.x) @@ -84,16 +91,10 @@ #defining inertia tensors for links -#Since links are rods, rotating axis= z-axis -#Hence, xx = yy = (1/12)*m*l**2 -i0 = (1.0/3)*M[0]*l[0]**2 -i1 = (1.0/3)*M[1]*l[1]**2 -i2 = (1.0/3)*M[2]*l[2]**2 - -inertia_link1 = inertia(A,i0,i0,0) -inertia_link2 = inertia(B,i1,i1,0) -inertia_link3 = inertia(C,i2,i2,0) +inertia_link1 = inertia(A,Ixx[0],Iyy[0],0) +inertia_link2 = inertia(B,Ixx[1],Iyy[1],0) +inertia_link3 = inertia(C,Ixx[2],Iyy[2],0) #Defining links as Rigid bodies ... @@ -118,7 +119,8 @@ forces.append((point, -mass * g * I.y) ) kinetic_differentials = [] for i in range(0,N_bobs): - kinetic_differentials.append(q[i].diff(t) - u[i]) + kinetic_differentials.append(alphad[i] - alpha[i]) + kinetic_differentials.append(betad[i] - beta[i]) #Adding particles and links in the same system ... total_system = [] @@ -128,6 +130,20 @@ for link in links: total_system.append(link) +q = [] +for angle in alpha: + q.append(angle) +for angle in beta: + q.append(angle) +print q +u = [] + +for vel in alphad: + u.append(vel) +for vel in betad: + u.append(vel) + +print u kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinetic_differentials) fr, frstar = kane.kanes_equations(forces, total_system) diff --git a/three_link_pendulum/three_link_pendulum_massless_links.py b/three_link_pendulum/three_link_pendulum_massless_links.py deleted file mode 100644 index 8b7561e..0000000 --- a/three_link_pendulum/three_link_pendulum_massless_links.py +++ /dev/null @@ -1,90 +0,0 @@ -#For this one we assume massless links -from sympy import symbols -from sympy.physics.mechanics import * - -#Number of masses = 3 -N_bobs = 3 - -#Defining Dynamic Symbols ................ - -#Generalized coordinates ... -q = dynamicsymbols('q:' + str(N_bobs)) - -#Generalized speeds ... -u = dynamicsymbols('u:' + str(N_links + 1)) - -#Mass of each bob: -m = symbols('m:'+str(N_bobs)) - -#Length of each link .. -l = symbols('l:' + str(N_links)) - - -#gravity and time .... -g, t = symbols('g t') - - -#Now defining an Inertial ReferenceFrame First .... - -I = ReferenceFrame('I') - -#Getting more referenceframes for RigidBodies ... - -A = I.orientnew('A', 'Axis', [q[0], I.z]) -B = I.orientnew('B', 'Axis', [q[1], I.z]) -C = I.orientnew('C', 'Axis', [q[2], I.z]) - -#Setting angular velocities of new frames ... -A.set_ang_vel(I, u[0] * I.z) -B.set_ang_vel(I, u[1] * I.z) -C.set_ang_vel(I, u[2] * I.z) - - - -# An Origin point, with velocity = 0 -O = Point('O') -O.set_vel(I,0) - -#Three more points, for particles .. -P1 = O.locatenew('P1', l[0] * A.x) -P2 = O.locatenew('P2', l[1] * B.x) -P3 = O.locatenew('P3', l[2] * C.x) - -#Setting velocities of points with v2pt theory ... -P1.v2pt_theory(O, I, A) -P2.v2pt_theory(P1, I, B) -P3.v2pt_theory(P2, I, C) -points = [P1,P2,P3] - -#Defining particles ... -Pa1 = Particle('Pa1', points[0], m[0]) -Pa2 = Particle('Pa2', points[1], m[1]) -Pa3 = Particle('Pa3', points[2], m[2]) -particles = [Pa1,Pa2,Pa3] - - - -#Applying forces on all particles , and adding all forces in a list.. -forces = [] -for particle in particles: - - mass = particle.get_mass() - point = particle.get_point() - forces.append((point, -mass * g * I.y) ) - - - - -print forces -kinetic_differentials = [] -for i in range(0,N_bobs): - kinetic_differentials.append(q[i].diff(t) - u[i]) - -print kinetic_differentials - -kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinetic_differentials) -fr, frstar = kane.kanes_equations(forces, particles) - -print(fr+frstar) - - From 89db91f2b447be6b20ae622a15b1c759685b2d95 Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Thu, 20 Jun 2013 01:35:41 +0530 Subject: [PATCH 05/33] Added an illustrative example to demonstrate the workflow of pydy_viz --- .../illustrative_example.py | 221 ++++++++++++++++++ .../three_link_pendulum.py | 157 +++++++++++++ three_link_pendulum/three_link_pendulum.py | 7 - 3 files changed, 378 insertions(+), 7 deletions(-) create mode 100644 illustrative_example_for_viz/illustrative_example.py create mode 100644 illustrative_example_for_viz/three_link_pendulum.py diff --git a/illustrative_example_for_viz/illustrative_example.py b/illustrative_example_for_viz/illustrative_example.py new file mode 100644 index 0000000..0486be9 --- /dev/null +++ b/illustrative_example_for_viz/illustrative_example.py @@ -0,0 +1,221 @@ +#This program represents a hypothetical situation for a complete workflow +#for simulating a three link pendulum with links as rigid bodies +from sympy import symbols,sympify +from sympy.physics.mechanics import * + +#Number of links = 3 +N_links = 3 + +#Number of masses = 3 +N_bobs = 3 + +#Defining Dynamic Symbols ................ + +#Generalized coordinates(angular) ... + +alpha = dynamicsymbols('alpha1 alpha2 alpha3') +beta = dynamicsymbols('beta1 beta2 beta3') + +#Generalized speeds(angular) ... +alphad = dynamicsymbols('alpha1 alpha2 alpha3',1) +betad = dynamicsymbols('beta1 beta2 beta3',1) + +#Mass of each bob: +m = symbols('m:'+str(N_bobs)) + + +#Length mass and radii of each link(assuming as rods) .. +l = symbols('l:' + str(N_links)) +M = symbols('M:' + str(N_links)) +radii = symbols('radii:' + str(N_links)) + +#For storing Inertia for each link : +Ixx = symbols('Ixx:'+str(N_links)) +Iyy = symbols('Iyy:'+str(N_links)) + +#gravity and time .... +g, t = symbols('g t') + + +#Now defining an Inertial ReferenceFrame First .... + +I = ReferenceFrame('I') + +#And some other frames ... + +A = ReferenceFrame('A') +A.orient(I,'Body',[alpha[0],beta[0],0],'ZXY') +B = ReferenceFrame('B') +B.orient(I,'Body',[alpha[1],beta[1],0],'ZXY') +C = ReferenceFrame('C') +C.orient(I,'Body',[alpha[2],beta[2],0],'ZXY') + + +#Setting angular velocities of new frames ... +A.set_ang_vel(I, alphad[0] * I.z + betad[0] * I.x) +B.set_ang_vel(I, alphad[1] * I.z + betad[1] * I.x) +C.set_ang_vel(I, alphad[2] * I.z + betad[2] * I.x) + + + +# An Origin point, with velocity = 0 +O = Point('O') +O.set_vel(I,0) + +#Three more points, for masses .. +P1 = O.locatenew('P1', l[0] * A.y) +P2 = O.locatenew('P2', l[1] * B.y) +P3 = O.locatenew('P3', l[2] * C.y) + +#Setting velocities of points with v2pt theory ... +P1.v2pt_theory(O, I, A) +P2.v2pt_theory(P1, I, B) +P3.v2pt_theory(P2, I, C) +points = [P1,P2,P3] + +Pa1 = Particle('Pa1', points[0], m[0]) +Pa2 = Particle('Pa2', points[1], m[1]) +Pa3 = Particle('Pa3', points[2], m[2]) +particles = [Pa1,Pa2,Pa3] + + + +#defining points for links(RigidBodies) +#Assuming CoM as l/2 ... +P_link1 = O.locatenew('P_link1', l[0]/2 * A.y) +P_link2 = O.locatenew('P_link1', l[1]/2 * B.y) +P_link3 = O.locatenew('P_link1', l[2]/2 * C.y) + +#setting velocities of these points with v2pt theory ... +P_link1.v2pt_theory(O, I, A) +P_link2.v2pt_theory(P_link1, I, B) +P_link3.v2pt_theory(P_link2, I, C) + +points_rigid_body = [P_link1,P_link2,P_link3] + + +#defining inertia tensors for links + +inertia_link1 = inertia(A,Ixx[0],Iyy[0],0) +inertia_link2 = inertia(B,Ixx[1],Iyy[1],0) +inertia_link3 = inertia(C,Ixx[2],Iyy[2],0) + +#Defining links as Rigid bodies ... + +link1 = RigidBody('link1', P_link1, A, M[0], (inertia_link1, O)) +link2 = RigidBody('link2', P_link2, B, M[1], (inertia_link2, P1)) +link3 = RigidBody('link3', P_link3, C, M[2], (inertia_link3, P2)) +links = [link1,link2,link3] + + +#Defining a basic shape for links .. +rod1 = Cylinder(length=l[0],radii=radii[0]) +rod2 = Cylinder(length=l[1],radii=radii[1]) +rod3 = Cylinder(length=l[2],radii=radii[2]) + +link1.shape(rod1) +link2.shape(rod2) +link3.shape(rod3) + +#Applying forces on all particles , and adding all forces in a list.. +forces = [] +for particle in particles: + + mass = particle.get_mass() + point = particle.get_point() + forces.append((point, -mass * g * I.y) ) + +#Applying forces on rigidbodies .. +for link in links: + mass = link.get_mass() + point = link.get_masscenter() + forces.append((point, -mass * g * I.y) ) + +kinetic_differentials = [] +for i in range(0,N_bobs): + kinetic_differentials.append(alphad[i] - alpha[i]) + kinetic_differentials.append(betad[i] - beta[i]) + +#Adding particles and links in the same system ... +total_system = [] +for particle in particles: + total_system.append(particle) + +for link in links: + total_system.append(link) + +q = [] +for angle in alpha: + q.append(angle) +for angle in beta: + q.append(angle) +print q +u = [] + +for vel in alphad: + u.append(vel) +for vel in betad: + u.append(vel) + +print u +kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinetic_differentials) +fr, frstar = kane.kanes_equations(forces, total_system) + +print fr + +#Now we have symbolic equations of motion. .. +# we integrate them numerically. .. + +params = [g ,l1,l2,l3,m1,m2,m3,M1,M2,M3] + +param_vals = [9.8 ,1.0,1.0,1.0,2,2,2,5,5,5] + +right_hand_side = code_generator(kane,params) + +#setting initial conditions .. +init_conditions = [radians(45),radians(45),radians(30),\ + radians(30),radians(15),radians(15),\ + 0, 0, 0,\ + 0, 0, 0] +t = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0] + +numerical_vals = odeint(right_hand_side,init_conditions,t) + +#Now for each t, we have numerical vals of coordinates .. +#Now we set up a visualization frame, + +frame1 = VisualizationFrame('frame1',I,O) + +frame1.add_rigidbodies(links) + +frame1.add_particles(particles) + +param_vals_for_viz = {'g':9.8 ,'l1':1.0,'l2':1.0,'l3':1.0,'m1':2,'m2':2,'m3':2,'M1':5,'M1':5,'M1':5] + +json = frame1.generate_json(initial_conditions,q) +#Here we can replace initial_conditions with the conditions at any +#specific time interval .... + +##This line does following things ... +##calls RigidBody.transform_matrix() on all rigidbodies, +#so that we have info of rigidbodies(CoM,rotation,translation) +# w.r.t VisualizationFrame('I' in this case) +##Even if they are defined in any other frame .... +##calls point.set_pos() for all particles with arg +##as Point in VisualizationFrame(O here) .. +##With these and init_conditions, we have a starting point of visualization .. + +scene = Scene() +Scene.view(json) # Just visualize/view the system at initial_conditions, + #w.r.t VIsualizationFrame(I in this case) + # No simulation here. .. + +Scene.simulate(json,numerical_vals) # modify the input json, + #Add the values at different times from numerical_vals, + #To the json, which is then passed to + #javascript + # + #(alpha1,alpha2,alpha3,beta1,beta2,beta3) at time=t + + + diff --git a/illustrative_example_for_viz/three_link_pendulum.py b/illustrative_example_for_viz/three_link_pendulum.py new file mode 100644 index 0000000..c5ec0aa --- /dev/null +++ b/illustrative_example_for_viz/three_link_pendulum.py @@ -0,0 +1,157 @@ +#For this one we assume RigidBody links +from sympy import symbols,sympify +from sympy.physics.mechanics import * + +#Number of links = 3 +N_links = 3 + +#Number of masses = 3 +N_bobs = 3 + +#Defining Dynamic Symbols ................ + +#Generalized coordinates(angular) ... + +alpha = dynamicsymbols('alpha1 alpha2 alpha3') +beta = dynamicsymbols('beta1 beta2 beta3') + +#Generalized speeds(angular) ... +alphad = dynamicsymbols('alpha1 alpha2 alpha3',1) +betad = dynamicsymbols('beta1 beta2 beta3',1) + +#Mass of each bob: +m = symbols('m:'+str(N_bobs)) + + +#Length and mass of each link .. +l = symbols('l:' + str(N_links)) +M = symbols('M:' + str(N_links)) +#For storing Inertia for each link : +Ixx = symbols('Ixx:'+str(N_links)) +Iyy = symbols('Iyy:'+str(N_links)) + +#gravity and time .... +g, t = symbols('g t') + + +#Now defining an Inertial ReferenceFrame First .... + +I = ReferenceFrame('I') + +#And some other frames ... + +A = ReferenceFrame('A') +A.orient(I,'Body',[alpha[0],beta[0],0],'ZXY') +B = ReferenceFrame('B') +B.orient(I,'Body',[alpha[1],beta[1],0],'ZXY') +C = ReferenceFrame('C') +C.orient(I,'Body',[alpha[2],beta[2],0],'ZXY') + + +#Setting angular velocities of new frames ... +A.set_ang_vel(I, alphad[0] * I.z + betad[0] * I.x) +B.set_ang_vel(I, alphad[1] * I.z + betad[1] * I.x) +C.set_ang_vel(I, alphad[2] * I.z + betad[2] * I.x) + + + +# An Origin point, with velocity = 0 +O = Point('O') +O.set_vel(I,0) + +#Three more points, for masses .. +P1 = O.locatenew('P1', l[0] * A.y) +P2 = O.locatenew('P2', l[1] * B.y) +P3 = O.locatenew('P3', l[2] * C.y) + +#Setting velocities of points with v2pt theory ... +P1.v2pt_theory(O, I, A) +P2.v2pt_theory(P1, I, B) +P3.v2pt_theory(P2, I, C) +points = [P1,P2,P3] + +Pa1 = Particle('Pa1', points[0], m[0]) +Pa2 = Particle('Pa2', points[1], m[1]) +Pa3 = Particle('Pa3', points[2], m[2]) +particles = [Pa1,Pa2,Pa3] + + + +#defining points for links(RigidBodies) +#Assuming CoM as l/2 ... +P_link1 = O.locatenew('P_link1', l[0]/2 * A.y) +P_link2 = O.locatenew('P_link1', l[1]/2 * B.y) +P_link3 = O.locatenew('P_link1', l[2]/2 * C.y) +#setting velocities of these points with v2pt theory ... +P_link1.v2pt_theory(O, I, A) +P_link2.v2pt_theory(P_link1, I, B) +P_link3.v2pt_theory(P_link2, I, C) + +points_rigid_body = [P_link1,P_link2,P_link3] + + +#defining inertia tensors for links + +inertia_link1 = inertia(A,Ixx[0],Iyy[0],0) +inertia_link2 = inertia(B,Ixx[1],Iyy[1],0) +inertia_link3 = inertia(C,Ixx[2],Iyy[2],0) + +#Defining links as Rigid bodies ... + +link1 = RigidBody('link1', P_link1, A, M[0], (inertia_link1, O)) +link2 = RigidBody('link2', P_link2, B, M[1], (inertia_link2, P1)) +link3 = RigidBody('link3', P_link3, C, M[2], (inertia_link3, P2)) +links = [link1,link2,link3] + + +#Applying forces on all particles , and adding all forces in a list.. +forces = [] +for particle in particles: + + mass = particle.get_mass() + point = particle.get_point() + forces.append((point, -mass * g * I.y) ) + +#Applying forces on rigidbodies .. +for link in links: + mass = link.get_mass() + point = link.get_masscenter() + forces.append((point, -mass * g * I.y) ) +kinetic_differentials = [] +for i in range(0,N_bobs): + kinetic_differentials.append(alphad[i] - alpha[i]) + kinetic_differentials.append(betad[i] - beta[i]) + +#Adding particles and links in the same system ... +total_system = [] +for particle in particles: + total_system.append(particle) + +for link in links: + total_system.append(link) + +q = [] +for angle in alpha: + q.append(angle) +for angle in beta: + q.append(angle) +print q +u = [] + +for vel in alphad: + u.append(vel) +for vel in betad: + u.append(vel) + +print u +kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinetic_differentials) +fr, frstar = kane.kanes_equations(forces, total_system) + +print fr + + + + + + + diff --git a/three_link_pendulum/three_link_pendulum.py b/three_link_pendulum/three_link_pendulum.py index c5ec0aa..169c1cd 100644 --- a/three_link_pendulum/three_link_pendulum.py +++ b/three_link_pendulum/three_link_pendulum.py @@ -148,10 +148,3 @@ fr, frstar = kane.kanes_equations(forces, total_system) print fr - - - - - - - From b10d0e5b4ce087d4cf17b809c44aec8804b94210 Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Sun, 23 Jun 2013 13:30:22 +0530 Subject: [PATCH 06/33] Updated to include code according to PEP8 style guide --- .../illustrative_example.py | 88 ++++++++++--------- 1 file changed, 46 insertions(+), 42 deletions(-) diff --git a/illustrative_example_for_viz/illustrative_example.py b/illustrative_example_for_viz/illustrative_example.py index 0486be9..090b12c 100644 --- a/illustrative_example_for_viz/illustrative_example.py +++ b/illustrative_example_for_viz/illustrative_example.py @@ -1,6 +1,6 @@ #This program represents a hypothetical situation for a complete workflow #for simulating a three link pendulum with links as rigid bodies -from sympy import symbols,sympify +from sympy import symbols, sympify from sympy.physics.mechanics import * #Number of links = 3 @@ -17,11 +17,11 @@ beta = dynamicsymbols('beta1 beta2 beta3') #Generalized speeds(angular) ... -alphad = dynamicsymbols('alpha1 alpha2 alpha3',1) -betad = dynamicsymbols('beta1 beta2 beta3',1) +vel_alpha = dynamicsymbols('vel_alpha1 vel_alpha2 vel_alpha3') +vel_beta = dynamicsymbols('vel_beta1 vel_beta2 vel_beta3') #Mass of each bob: -m = symbols('m:'+str(N_bobs)) +m = symbols('m:' + str(N_bobs)) #Length mass and radii of each link(assuming as rods) .. @@ -30,8 +30,12 @@ radii = symbols('radii:' + str(N_links)) #For storing Inertia for each link : -Ixx = symbols('Ixx:'+str(N_links)) -Iyy = symbols('Iyy:'+str(N_links)) +Ixx = symbols('Ixx:' + str(N_links)) +Iyy = symbols('Iyy:' + str(N_links)) +Izz = symbols('Izz:' + str(N_links)) +Ixy = symbols('Ixy:' + str(N_links)) +Iyz = symbols('Iyz:' + str(N_links)) +Ixz = symbols('Ixz:' + str(N_links)) #gravity and time .... g, t = symbols('g t') @@ -43,24 +47,21 @@ #And some other frames ... -A = ReferenceFrame('A') -A.orient(I,'Body',[alpha[0],beta[0],0],'ZXY') -B = ReferenceFrame('B') -B.orient(I,'Body',[alpha[1],beta[1],0],'ZXY') -C = ReferenceFrame('C') -C.orient(I,'Body',[alpha[2],beta[2],0],'ZXY') +A = I.orientnew('A', 'Body', [alpha[0], beta[0], 0], 'ZXY') +B = A.orientnew('B', 'Body', [alpha[1], beta[1], 0], 'ZXY') +C = B.orientnew('C', 'Body', [alpha[2], beta[2], 0], 'ZXY') #Setting angular velocities of new frames ... -A.set_ang_vel(I, alphad[0] * I.z + betad[0] * I.x) -B.set_ang_vel(I, alphad[1] * I.z + betad[1] * I.x) -C.set_ang_vel(I, alphad[2] * I.z + betad[2] * I.x) +A.set_ang_vel(I, vel_alpha[0] * I.z + vel_beta[0] * I.x) +B.set_ang_vel(A, vel_alpha[1] * A.z + vel_beta[1] * A.x) +C.set_ang_vel(B, vel_alpha[2] * B.z + vel_beta[2] * B.x) # An Origin point, with velocity = 0 O = Point('O') -O.set_vel(I,0) +O.set_vel(I, 0) #Three more points, for masses .. P1 = O.locatenew('P1', l[0] * A.y) @@ -71,12 +72,12 @@ P1.v2pt_theory(O, I, A) P2.v2pt_theory(P1, I, B) P3.v2pt_theory(P2, I, C) -points = [P1,P2,P3] +points = [P1, P2, P3] Pa1 = Particle('Pa1', points[0], m[0]) Pa2 = Particle('Pa2', points[1], m[1]) Pa3 = Particle('Pa3', points[2], m[2]) -particles = [Pa1,Pa2,Pa3] +particles = [Pa1, Pa2, Pa3] @@ -91,14 +92,15 @@ P_link2.v2pt_theory(P_link1, I, B) P_link3.v2pt_theory(P_link2, I, C) -points_rigid_body = [P_link1,P_link2,P_link3] +points_rigid_body = [P_link1, P_link2, P_link3] #defining inertia tensors for links -inertia_link1 = inertia(A,Ixx[0],Iyy[0],0) -inertia_link2 = inertia(B,Ixx[1],Iyy[1],0) -inertia_link3 = inertia(C,Ixx[2],Iyy[2],0) + +inertia_link1 = inertia(A, Ixx[0], Iyy[0], Izz[0], ixy = Ixy[0], iyz = Iyz[0], izx = Ixz[0]) +inertia_link2 = inertia(B, Ixx[1], Iyy[1], Izz[1], ixy = Ixy[1], iyz = Iyz[1], izx = Ixz[1]) +inertia_link3 = inertia(C, Ixx[2], Iyy[2], Izz[2], ixy = Ixy[2], iyz = Iyz[2], izx = Ixz[2]) #Defining links as Rigid bodies ... @@ -109,9 +111,9 @@ #Defining a basic shape for links .. -rod1 = Cylinder(length=l[0],radii=radii[0]) -rod2 = Cylinder(length=l[1],radii=radii[1]) -rod3 = Cylinder(length=l[2],radii=radii[2]) +rod1 = Cylinder(length = l[0], radii = radii[0]) +rod2 = Cylinder(length = l[1], radii = radii[1]) +rod3 = Cylinder(length = l[2], radii = radii[2]) link1.shape(rod1) link2.shape(rod2) @@ -133,8 +135,8 @@ kinetic_differentials = [] for i in range(0,N_bobs): - kinetic_differentials.append(alphad[i] - alpha[i]) - kinetic_differentials.append(betad[i] - beta[i]) + kinetic_differentials.append(vel_alpha[i] - alpha[i].diff(t)) + kinetic_differentials.append(vel_betad[i] - beta[i].diff(t)) #Adding particles and links in the same system ... total_system = [] @@ -146,19 +148,19 @@ q = [] for angle in alpha: - q.append(angle) + q.append(angle) for angle in beta: - q.append(angle) + q.append(angle) print q u = [] -for vel in alphad: - u.append(vel) -for vel in betad: - u.append(vel) +for vel in vel_alpha: + u.append(vel) +for vel in vel_beta: + u.append(vel) print u -kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinetic_differentials) +kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs = kinetic_differentials) fr, frstar = kane.kanes_equations(forces, total_system) print fr @@ -166,9 +168,9 @@ #Now we have symbolic equations of motion. .. # we integrate them numerically. .. -params = [g ,l1,l2,l3,m1,m2,m3,M1,M2,M3] +params = [g ,l1, l2, l3, m1, m2, m3, M1, M2, M3] -param_vals = [9.8 ,1.0,1.0,1.0,2,2,2,5,5,5] +param_vals = [9.8 ,1.0, 1.0, 1.0, 2, 2, 2, 5, 5, 5] right_hand_side = code_generator(kane,params) @@ -177,22 +179,24 @@ radians(30),radians(15),radians(15),\ 0, 0, 0,\ 0, 0, 0] -t = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0] +t = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0] -numerical_vals = odeint(right_hand_side,init_conditions,t) +numerical_vals = odeint(right_hand_side, init_conditions, t) #Now for each t, we have numerical vals of coordinates .. #Now we set up a visualization frame, -frame1 = VisualizationFrame('frame1',I,O) +frame1 = VisualizationFrame('frame1',I , O) frame1.add_rigidbodies(links) frame1.add_particles(particles) -param_vals_for_viz = {'g':9.8 ,'l1':1.0,'l2':1.0,'l3':1.0,'m1':2,'m2':2,'m3':2,'M1':5,'M1':5,'M1':5] +param_vals_for_viz = {'g':9.8, 'l1':1.0, 'l2':1.0, \ + 'l3':1.0, 'm1':2, 'm2':2, 'm3':2, \ + 'M1':5, 'M1':5, 'M1':5] -json = frame1.generate_json(initial_conditions,q) +json = frame1.generate_json(initial_conditions, q) #Here we can replace initial_conditions with the conditions at any #specific time interval .... @@ -210,7 +214,7 @@ #w.r.t VIsualizationFrame(I in this case) # No simulation here. .. -Scene.simulate(json,numerical_vals) # modify the input json, +Scene.simulate(json, numerical_vals) # modify the input json, #Add the values at different times from numerical_vals, #To the json, which is then passed to #javascript From b1a923c1414396a3bcabd7378f5b649dee7b8814 Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Tue, 9 Jul 2013 18:56:51 +0530 Subject: [PATCH 07/33] [WIP] Added some base classes for the illustrative example --- illustrative_example_for_viz/essential.py | 99 ++++++++ .../illustrative_example.py | 238 ++---------------- 2 files changed, 121 insertions(+), 216 deletions(-) create mode 100644 illustrative_example_for_viz/essential.py diff --git a/illustrative_example_for_viz/essential.py b/illustrative_example_for_viz/essential.py new file mode 100644 index 0000000..d72c6e1 --- /dev/null +++ b/illustrative_example_for_viz/essential.py @@ -0,0 +1,99 @@ +#This file contains all the essential methods for the +#illustrative example +#It only contains the basic implementations of pydy-viz +#also it doesnot check for TypeErrors etc. + +class MeshShape(object): + def __init__(self,name,point_list,color='grey',origin=[0,0,0]): + self._name = name + self._points = point_list + self._color = color + self._origin = origin + + @property + def name(self): + return self._name + + @name.setter + def name(self,new_name): + self._name = new_name + + @property + def points(self): + return self._points + + @points.setter + def points(self,new_point_list): + self._points = new_point_list + + @property + def color(self): + return self._color + + @color.setter + def color(self,new_color): + self._color = new_color + + @property + def origin(self): + return self._origin + + @color.setter + def origin(self,new_origin): + self._origin = new_origin + + +class VisualizationFrame(object): + def __init__(self,name,rigidbody,shape=None): + #It is only to be used for rigidbody here, as per the + #specific requirements of the illustrative example + self._name = name + self._reference_frame = rigidbody.get_frame() + self._point = rigidbody.get_masscenter() + self._shape = shape + self._transformation_matrix = \ + [[1, 0, 0, 0], \ + [0, 1, 0, 0], \ + [0, 0, 1, 0], \ + [0, 0, 0, 1]] + + def homogeneous_transformation(self,rframe): + rotation_matrix = self._reference_frame.dcm(rframe) + for i in range(0,3): + for j in range(0,3): + self._transformation_matrix[i][j] = rotation_matrix + return self._transformation_matrix + + def add_simulation_data(self,file_name=None): + #TODO + pass + + def generate_json(): + #TODO + pass + +class Scene(): + def __init__(self,name,reference_frame,origin,height=800,width=800): + self._name = name + self._reference_frame=reference_frame + self._origin = origin #contains point + self._child_vframes = [] + self._height = height + self._width = width + + @property + def vframes(self): + return self._child_vframes + @vframes.setter + def vframes(self,vframes): + for vframe in vframes: + self._child_vframes.append(vframe) + + + def generate_json(self): + #TODO + pass + + + + diff --git a/illustrative_example_for_viz/illustrative_example.py b/illustrative_example_for_viz/illustrative_example.py index 090b12c..fc71cb4 100644 --- a/illustrative_example_for_viz/illustrative_example.py +++ b/illustrative_example_for_viz/illustrative_example.py @@ -1,225 +1,31 @@ -#This program represents a hypothetical situation for a complete workflow -#for simulating a three link pendulum with links as rigid bodies -from sympy import symbols, sympify -from sympy.physics.mechanics import * +#Export method calls and namespace +# from three_link_pendulum example .. -#Number of links = 3 -N_links = 3 +from three_link_pendulum import * +from essential import * -#Number of masses = 3 -N_bobs = 3 +#setting some shapes for the pendulums .. -#Defining Dynamic Symbols ................ +shape1 = MeshShape('shape1',[[1,1,1], [0,1,1], [2,1,1]], \ + color='red',origin=[0,0,0]) -#Generalized coordinates(angular) ... +shape2 = MeshShape('shape2',[[1,1,1], [0,1,1], [2,1,1]], \ + color='blue',origin=[0,0,0]) + +shape3 = MeshShape('shape3',[[1,1,1], [0,1,1], [2,1,1]], \ + color='green',origin=[0,0,0]) -alpha = dynamicsymbols('alpha1 alpha2 alpha3') -beta = dynamicsymbols('beta1 beta2 beta3') +#Setting up some vframes ... + +frame1 = VisualizationFrame('frame1', link1, shape=shape1) +print frame1.homogeneous_transformation(I) -#Generalized speeds(angular) ... -vel_alpha = dynamicsymbols('vel_alpha1 vel_alpha2 vel_alpha3') -vel_beta = dynamicsymbols('vel_beta1 vel_beta2 vel_beta3') - -#Mass of each bob: -m = symbols('m:' + str(N_bobs)) - - -#Length mass and radii of each link(assuming as rods) .. -l = symbols('l:' + str(N_links)) -M = symbols('M:' + str(N_links)) -radii = symbols('radii:' + str(N_links)) - -#For storing Inertia for each link : -Ixx = symbols('Ixx:' + str(N_links)) -Iyy = symbols('Iyy:' + str(N_links)) -Izz = symbols('Izz:' + str(N_links)) -Ixy = symbols('Ixy:' + str(N_links)) -Iyz = symbols('Iyz:' + str(N_links)) -Ixz = symbols('Ixz:' + str(N_links)) - -#gravity and time .... -g, t = symbols('g t') - - -#Now defining an Inertial ReferenceFrame First .... - -I = ReferenceFrame('I') - -#And some other frames ... - -A = I.orientnew('A', 'Body', [alpha[0], beta[0], 0], 'ZXY') -B = A.orientnew('B', 'Body', [alpha[1], beta[1], 0], 'ZXY') -C = B.orientnew('C', 'Body', [alpha[2], beta[2], 0], 'ZXY') - - -#Setting angular velocities of new frames ... -A.set_ang_vel(I, vel_alpha[0] * I.z + vel_beta[0] * I.x) -B.set_ang_vel(A, vel_alpha[1] * A.z + vel_beta[1] * A.x) -C.set_ang_vel(B, vel_alpha[2] * B.z + vel_beta[2] * B.x) - - - -# An Origin point, with velocity = 0 -O = Point('O') -O.set_vel(I, 0) - -#Three more points, for masses .. -P1 = O.locatenew('P1', l[0] * A.y) -P2 = O.locatenew('P2', l[1] * B.y) -P3 = O.locatenew('P3', l[2] * C.y) - -#Setting velocities of points with v2pt theory ... -P1.v2pt_theory(O, I, A) -P2.v2pt_theory(P1, I, B) -P3.v2pt_theory(P2, I, C) -points = [P1, P2, P3] - -Pa1 = Particle('Pa1', points[0], m[0]) -Pa2 = Particle('Pa2', points[1], m[1]) -Pa3 = Particle('Pa3', points[2], m[2]) -particles = [Pa1, Pa2, Pa3] - - - -#defining points for links(RigidBodies) -#Assuming CoM as l/2 ... -P_link1 = O.locatenew('P_link1', l[0]/2 * A.y) -P_link2 = O.locatenew('P_link1', l[1]/2 * B.y) -P_link3 = O.locatenew('P_link1', l[2]/2 * C.y) - -#setting velocities of these points with v2pt theory ... -P_link1.v2pt_theory(O, I, A) -P_link2.v2pt_theory(P_link1, I, B) -P_link3.v2pt_theory(P_link2, I, C) - -points_rigid_body = [P_link1, P_link2, P_link3] - - -#defining inertia tensors for links - - -inertia_link1 = inertia(A, Ixx[0], Iyy[0], Izz[0], ixy = Ixy[0], iyz = Iyz[0], izx = Ixz[0]) -inertia_link2 = inertia(B, Ixx[1], Iyy[1], Izz[1], ixy = Ixy[1], iyz = Iyz[1], izx = Ixz[1]) -inertia_link3 = inertia(C, Ixx[2], Iyy[2], Izz[2], ixy = Ixy[2], iyz = Iyz[2], izx = Ixz[2]) - -#Defining links as Rigid bodies ... - -link1 = RigidBody('link1', P_link1, A, M[0], (inertia_link1, O)) -link2 = RigidBody('link2', P_link2, B, M[1], (inertia_link2, P1)) -link3 = RigidBody('link3', P_link3, C, M[2], (inertia_link3, P2)) -links = [link1,link2,link3] - - -#Defining a basic shape for links .. -rod1 = Cylinder(length = l[0], radii = radii[0]) -rod2 = Cylinder(length = l[1], radii = radii[1]) -rod3 = Cylinder(length = l[2], radii = radii[2]) - -link1.shape(rod1) -link2.shape(rod2) -link3.shape(rod3) - -#Applying forces on all particles , and adding all forces in a list.. -forces = [] -for particle in particles: - - mass = particle.get_mass() - point = particle.get_point() - forces.append((point, -mass * g * I.y) ) - -#Applying forces on rigidbodies .. -for link in links: - mass = link.get_mass() - point = link.get_masscenter() - forces.append((point, -mass * g * I.y) ) - -kinetic_differentials = [] -for i in range(0,N_bobs): - kinetic_differentials.append(vel_alpha[i] - alpha[i].diff(t)) - kinetic_differentials.append(vel_betad[i] - beta[i].diff(t)) - -#Adding particles and links in the same system ... -total_system = [] -for particle in particles: - total_system.append(particle) - -for link in links: - total_system.append(link) - -q = [] -for angle in alpha: - q.append(angle) -for angle in beta: - q.append(angle) -print q -u = [] - -for vel in vel_alpha: - u.append(vel) -for vel in vel_beta: - u.append(vel) - -print u -kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs = kinetic_differentials) -fr, frstar = kane.kanes_equations(forces, total_system) - -print fr - -#Now we have symbolic equations of motion. .. -# we integrate them numerically. .. - -params = [g ,l1, l2, l3, m1, m2, m3, M1, M2, M3] - -param_vals = [9.8 ,1.0, 1.0, 1.0, 2, 2, 2, 5, 5, 5] - -right_hand_side = code_generator(kane,params) - -#setting initial conditions .. -init_conditions = [radians(45),radians(45),radians(30),\ - radians(30),radians(15),radians(15),\ - 0, 0, 0,\ - 0, 0, 0] -t = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0] - -numerical_vals = odeint(right_hand_side, init_conditions, t) - -#Now for each t, we have numerical vals of coordinates .. -#Now we set up a visualization frame, - -frame1 = VisualizationFrame('frame1',I , O) - -frame1.add_rigidbodies(links) - -frame1.add_particles(particles) - -param_vals_for_viz = {'g':9.8, 'l1':1.0, 'l2':1.0, \ - 'l3':1.0, 'm1':2, 'm2':2, 'm3':2, \ - 'M1':5, 'M1':5, 'M1':5] - -json = frame1.generate_json(initial_conditions, q) -#Here we can replace initial_conditions with the conditions at any -#specific time interval .... - -##This line does following things ... -##calls RigidBody.transform_matrix() on all rigidbodies, -#so that we have info of rigidbodies(CoM,rotation,translation) -# w.r.t VisualizationFrame('I' in this case) -##Even if they are defined in any other frame .... -##calls point.set_pos() for all particles with arg -##as Point in VisualizationFrame(O here) .. -##With these and init_conditions, we have a starting point of visualization .. - -scene = Scene() -Scene.view(json) # Just visualize/view the system at initial_conditions, - #w.r.t VIsualizationFrame(I in this case) - # No simulation here. .. - -Scene.simulate(json, numerical_vals) # modify the input json, - #Add the values at different times from numerical_vals, - #To the json, which is then passed to - #javascript - # - #(alpha1,alpha2,alpha3,beta1,beta2,beta3) at time=t +frame2 = VisualizationFrame('frame2', link2, shape=shape2) +frame3 = VisualizationFrame('frame3', link3, shape=shape3) +scene = Scene('scene1',I,O) +scene.vframes = [frame1,frame2,frame3] +print scene.vframes +scene.generate_json() From aa6a338f18bb3e25e921fc5072eb2177e26b8449 Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Wed, 10 Jul 2013 19:14:14 +0530 Subject: [PATCH 08/33] [WIP] Some error in the numerical integration of the problem. run illustrative_example.py to see what is wrong --- illustrative_example_for_viz/code_gen.py | 52 +++++++++++++++++++ illustrative_example_for_viz/essential.py | 48 +++++++---------- .../illustrative_example.py | 3 +- .../three_link_pendulum.py | 43 ++++++++++++--- mass_spring/code_gen.py | 0 5 files changed, 109 insertions(+), 37 deletions(-) create mode 100755 illustrative_example_for_viz/code_gen.py mode change 100755 => 100644 mass_spring/code_gen.py diff --git a/illustrative_example_for_viz/code_gen.py b/illustrative_example_for_viz/code_gen.py new file mode 100755 index 0000000..8096e1c --- /dev/null +++ b/illustrative_example_for_viz/code_gen.py @@ -0,0 +1,52 @@ +#!/usr/bin/env python + +from sympy import Dummy, lambdify +from sympy.external import import_module + +np = import_module('numpy') + +def numeric_right_hand_side(kane, parameters): + """Returns the right hand side of the first order ordinary differential + equations from a KanesMethod system which can be evaluated numerically. + + This function probably only works for simple cases (no dependent speeds, + specified functions). + + """ + + dynamic = kane._q + kane._u + dummy_symbols = [Dummy() for i in dynamic] + dummy_dict = dict(zip(dynamic, dummy_symbols)) + kindiff_dict = kane.kindiffdict() + + M = kane.mass_matrix_full.subs(kindiff_dict).subs(dummy_dict) + F = kane.forcing_full.subs(kindiff_dict).subs(dummy_dict) + + M_func = lambdify(dummy_symbols + parameters, M) + F_func = lambdify(dummy_symbols + parameters, F) + + def right_hand_side(x, t, args): + """Returns the derivatives of the states. + + Parameters + ---------- + x : ndarray, shape(n) + The current state vector. + t : float + The current time. + args : ndarray + The constants. + + Returns + ------- + dx : ndarray, shape(2 * (n + 1)) + The derivative of the state. + + """ + arguments = np.hstack((x, args)) + dx = np.array(np.linalg.solve(M_func(*arguments), + F_func(*arguments))).T[0] + + return dx + + return right_hand_side \ No newline at end of file diff --git a/illustrative_example_for_viz/essential.py b/illustrative_example_for_viz/essential.py index d72c6e1..60eb7f0 100644 --- a/illustrative_example_for_viz/essential.py +++ b/illustrative_example_for_viz/essential.py @@ -2,9 +2,10 @@ #illustrative example #It only contains the basic implementations of pydy-viz #also it doesnot check for TypeErrors etc. +import numpy as np class MeshShape(object): - def __init__(self,name,point_list,color='grey',origin=[0,0,0]): + def __init__(self, name, point_list, color='grey', origin=[0,0,0]): self._name = name self._points = point_list self._color = color @@ -15,7 +16,7 @@ def name(self): return self._name @name.setter - def name(self,new_name): + def name(self, new_name): self._name = new_name @property @@ -23,7 +24,7 @@ def points(self): return self._points @points.setter - def points(self,new_point_list): + def points(self, new_point_list): self._points = new_point_list @property @@ -31,7 +32,7 @@ def color(self): return self._color @color.setter - def color(self,new_color): + def color(self, new_color): self._color = new_color @property @@ -39,30 +40,24 @@ def origin(self): return self._origin @color.setter - def origin(self,new_origin): + def origin(self, new_origin): self._origin = new_origin class VisualizationFrame(object): - def __init__(self,name,rigidbody,shape=None): + def __init__(self, name, rigidbody, shape=None): #It is only to be used for rigidbody here, as per the #specific requirements of the illustrative example self._name = name self._reference_frame = rigidbody.get_frame() - self._point = rigidbody.get_masscenter() + self._origin = rigidbody.get_masscenter() self._shape = shape - self._transformation_matrix = \ - [[1, 0, 0, 0], \ - [0, 1, 0, 0], \ - [0, 0, 1, 0], \ - [0, 0, 0, 1]] + self._transform = np.eye(4) - def homogeneous_transformation(self,rframe): + def transform(self,rframe): rotation_matrix = self._reference_frame.dcm(rframe) - for i in range(0,3): - for j in range(0,3): - self._transformation_matrix[i][j] = rotation_matrix - return self._transformation_matrix + self._transform[0:3,0:3] = rotation_matrix + return self._transform def add_simulation_data(self,file_name=None): #TODO @@ -81,19 +76,16 @@ def __init__(self,name,reference_frame,origin,height=800,width=800): self._height = height self._width = width - @property - def vframes(self): - return self._child_vframes - @vframes.setter - def vframes(self,vframes): - for vframe in vframes: - self._child_vframes.append(vframe) + + def add_visualization_frames(self,vframes): + for _vframe in vframes: + self._child_vframes.append(_vframe) + + def add_visualization_frame(self,vframe): + self._child_vframes.append(vframe) def generate_json(self): #TODO pass - - - - + diff --git a/illustrative_example_for_viz/illustrative_example.py b/illustrative_example_for_viz/illustrative_example.py index fc71cb4..70b0a56 100644 --- a/illustrative_example_for_viz/illustrative_example.py +++ b/illustrative_example_for_viz/illustrative_example.py @@ -24,8 +24,7 @@ frame3 = VisualizationFrame('frame3', link3, shape=shape3) scene = Scene('scene1',I,O) -scene.vframes = [frame1,frame2,frame3] -print scene.vframes +scene.add_visualization_frame([frame1,frame2,frame3]) scene.generate_json() diff --git a/illustrative_example_for_viz/three_link_pendulum.py b/illustrative_example_for_viz/three_link_pendulum.py index c5ec0aa..c1a98bc 100644 --- a/illustrative_example_for_viz/three_link_pendulum.py +++ b/illustrative_example_for_viz/three_link_pendulum.py @@ -1,7 +1,8 @@ #For this one we assume RigidBody links from sympy import symbols,sympify from sympy.physics.mechanics import * - +from code_gen import * +from scipy.integrate import odeint #Number of links = 3 N_links = 3 @@ -29,6 +30,7 @@ #For storing Inertia for each link : Ixx = symbols('Ixx:'+str(N_links)) Iyy = symbols('Iyy:'+str(N_links)) +Izz = symbols('Izz:'+str(N_links)) #gravity and time .... g, t = symbols('g t') @@ -92,9 +94,9 @@ #defining inertia tensors for links -inertia_link1 = inertia(A,Ixx[0],Iyy[0],0) -inertia_link2 = inertia(B,Ixx[1],Iyy[1],0) -inertia_link3 = inertia(C,Ixx[2],Iyy[2],0) +inertia_link1 = inertia(A,Ixx[0],Iyy[0],Izz[0]) +inertia_link2 = inertia(B,Ixx[1],Iyy[1],Izz[1]) +inertia_link3 = inertia(C,Ixx[2],Iyy[2],Izz[2]) #Defining links as Rigid bodies ... @@ -135,22 +137,49 @@ q.append(angle) for angle in beta: q.append(angle) -print q -u = [] +u = [] for vel in alphad: u.append(vel) for vel in betad: u.append(vel) -print u + kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinetic_differentials) fr, frstar = kane.kanes_equations(forces, total_system) print fr +#Now we do numerical integration on the Kane object obtained ... +params = [] +for lengths in l: + params.append(lengths) + +for masses in m: + params.append(masses) + +for masses in M: + params.append(masses) + +for inertias in Ixx: + params.append(inertias) + +for inertias in Iyy: + params.append(inertias) + +for inertias in Izz: + params.append(inertias) +params.append(g) + +print params +right_hand_side = numeric_right_hand_side(kane, params) +param_vals = [10, 10, 10, 5, 5, 5, 10, 10, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9.8] +t = [i*1 for i in range(0,10)] #Taking 10 time intervals of 0.1 sec +x0 = [45,45,45,45,45,45,0,0,0,0,0,0] +numeric_vals = odeint(right_hand_side, x0, t, args=(param_vals,)) +print numeric_vals diff --git a/mass_spring/code_gen.py b/mass_spring/code_gen.py old mode 100755 new mode 100644 From 17f8f0b880f0da3eae6796d2d181f810511a964d Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Fri, 12 Jul 2013 13:12:02 +0530 Subject: [PATCH 09/33] WIP --- illustrative_example_for_viz/essential.py | 34 +++++++--- .../illustrative_example.py | 12 +++- illustrative_example_for_viz/simulate.py | 67 +++++++++++++++++++ .../three_link_pendulum.py | 57 ++++------------ 4 files changed, 112 insertions(+), 58 deletions(-) create mode 100644 illustrative_example_for_viz/simulate.py diff --git a/illustrative_example_for_viz/essential.py b/illustrative_example_for_viz/essential.py index 60eb7f0..fa2aa69 100644 --- a/illustrative_example_for_viz/essential.py +++ b/illustrative_example_for_viz/essential.py @@ -3,6 +3,7 @@ #It only contains the basic implementations of pydy-viz #also it doesnot check for TypeErrors etc. import numpy as np +from sympy.matrices.expressions import Identity class MeshShape(object): def __init__(self, name, point_list, color='grey', origin=[0,0,0]): @@ -52,20 +53,30 @@ def __init__(self, name, rigidbody, shape=None): self._reference_frame = rigidbody.get_frame() self._origin = rigidbody.get_masscenter() self._shape = shape - self._transform = np.eye(4) + self._transform = Identity(4).as_mutable() + + def transform(self, reference_frame, point): + _rotation_matrix = self._reference_frame.dcm(reference_frame) + + self._transform[0:3,0:3] = _rotation_matrix[0:3,0:3] + + _point_vector = self._origin.pos_from(point).express(reference_frame) + + self._transform[0,3] = _point_vector.dot(reference_frame.x) + self._transform[1,3] = _point_vector.dot(reference_frame.y) + self._transform[2,3] = _point_vector.dot(reference_frame.z) - def transform(self,rframe): - rotation_matrix = self._reference_frame.dcm(rframe) - self._transform[0:3,0:3] = rotation_matrix return self._transform + + def eval_transform(self): + self._numerical_transform = self._transform.evalf(subs=vel_dict) + return self._numerical_transform - def add_simulation_data(self,file_name=None): - #TODO - pass - - def generate_json(): - #TODO - pass + def generate_simulation_data(self,values_list,timesteps=None): + self.simulation_matrix = [] + for iterator in range(0,timesteps): + self.simulation_matrix.append(self._transform.evalf(subs=values_list[iterator])) + return self.simulation_matrix class Scene(): def __init__(self,name,reference_frame,origin,height=800,width=800): @@ -86,6 +97,7 @@ def add_visualization_frame(self,vframe): def generate_json(self): + #TODO pass diff --git a/illustrative_example_for_viz/illustrative_example.py b/illustrative_example_for_viz/illustrative_example.py index 70b0a56..178e2a6 100644 --- a/illustrative_example_for_viz/illustrative_example.py +++ b/illustrative_example_for_viz/illustrative_example.py @@ -1,9 +1,8 @@ #Export method calls and namespace # from three_link_pendulum example .. -from three_link_pendulum import * from essential import * - +from simulate import * #setting some shapes for the pendulums .. shape1 = MeshShape('shape1',[[1,1,1], [0,1,1], [2,1,1]], \ @@ -18,9 +17,16 @@ #Setting up some vframes ... frame1 = VisualizationFrame('frame1', link1, shape=shape1) -print frame1.homogeneous_transformation(I) + +#Now these methods would be called from within Scene for generating +#simulation data, similar for all frames +frame1.transform(I,O) +simulation_matrix1 = frame1.generate_simulation_data(values_list,timesteps=100) +print simulation_matrix1 + frame2 = VisualizationFrame('frame2', link2, shape=shape2) + frame3 = VisualizationFrame('frame3', link3, shape=shape3) scene = Scene('scene1',I,O) diff --git a/illustrative_example_for_viz/simulate.py b/illustrative_example_for_viz/simulate.py new file mode 100644 index 0000000..9af669f --- /dev/null +++ b/illustrative_example_for_viz/simulate.py @@ -0,0 +1,67 @@ +#THis script produces the numerical integration for the EoMs +#generated by three_link_pendulum.py + +from three_link_pendulum import * +from scipy.integrate import odeint +from code_gen import * +from numpy import radians + +params = [] +param_vals = [] +for lengths in l: + params.append(lengths) + param_vals.append(10) + +for masses in m: + params.append(masses) + param_vals.append(5) + +for masses in M: + params.append(masses) + param_vals.append(10) + +for inertias in Ixx: + params.append(inertias) + param_vals.append(5) + +for inertias in Iyy: + params.append(inertias) + param_vals.append(5) + +for inertias in Izz: + params.append(inertias) + param_vals.append(5) + +params.append(g) +param_vals.append(9.8) + +print params +print param_vals +right_hand_side = numeric_right_hand_side(kane, params) + +t = [i*0.1 for i in range(0,100)] #Taking 10 time intervals of 0.1 sec + +x0 = [radians(10), radians(10), radians(10), radians(10), radians(10), \ + radians(10), radians(10), 0, 0, 0, 0, 0] + +numeric_vals = odeint(right_hand_side, x0, t, args=(param_vals,)) + + +#mapping in a dict: +values_list = [] + +for val in numeric_vals: + val_dict = {} + val_dict[alpha[0]] = val[0] + val_dict[alpha[1]] = val[1] + val_dict[alpha[2]] = val[2] + val_dict[beta[0]] = val[3] + val_dict[beta[1]] = val[4] + val_dict[beta[2]] = val[5] + #Since lengths are also used in defining some positions ... + val_dict[l[0]] = 10 + val_dict[l[1]] = 10 + val_dict[l[2]] = 10 + values_list.append(val_dict) + +print values_list[0] diff --git a/illustrative_example_for_viz/three_link_pendulum.py b/illustrative_example_for_viz/three_link_pendulum.py index c1a98bc..4fb3ce3 100644 --- a/illustrative_example_for_viz/three_link_pendulum.py +++ b/illustrative_example_for_viz/three_link_pendulum.py @@ -1,8 +1,8 @@ + #For this one we assume RigidBody links from sympy import symbols,sympify from sympy.physics.mechanics import * -from code_gen import * -from scipy.integrate import odeint + #Number of links = 3 N_links = 3 @@ -17,8 +17,8 @@ beta = dynamicsymbols('beta1 beta2 beta3') #Generalized speeds(angular) ... -alphad = dynamicsymbols('alpha1 alpha2 alpha3',1) -betad = dynamicsymbols('beta1 beta2 beta3',1) +omega = dynamicsymbols('omega1 omega2 omega3') +delta = dynamicsymbols('delta1 delta2 delta3') #Mass of each bob: m = symbols('m:'+str(N_bobs)) @@ -51,9 +51,9 @@ #Setting angular velocities of new frames ... -A.set_ang_vel(I, alphad[0] * I.z + betad[0] * I.x) -B.set_ang_vel(I, alphad[1] * I.z + betad[1] * I.x) -C.set_ang_vel(I, alphad[2] * I.z + betad[2] * I.x) +A.set_ang_vel(I, omega[0] * I.z + delta[0] * I.x) +B.set_ang_vel(I, omega[1] * I.z + delta[1] * I.x) +C.set_ang_vel(I, omega[2] * I.z + delta[2] * I.x) @@ -119,10 +119,10 @@ mass = link.get_mass() point = link.get_masscenter() forces.append((point, -mass * g * I.y) ) -kinetic_differentials = [] +kinematic_differentials = [] for i in range(0,N_bobs): - kinetic_differentials.append(alphad[i] - alpha[i]) - kinetic_differentials.append(betad[i] - beta[i]) + kinematic_differentials.append(omega[i] - alpha[i].diff(t)) + kinematic_differentials.append(delta[i] - beta[i].diff(t)) #Adding particles and links in the same system ... total_system = [] @@ -139,48 +139,17 @@ q.append(angle) u = [] -for vel in alphad: +for vel in omega: u.append(vel) -for vel in betad: +for vel in delta: u.append(vel) -kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinetic_differentials) +kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinematic_differentials) fr, frstar = kane.kanes_equations(forces, total_system) print fr -#Now we do numerical integration on the Kane object obtained ... -params = [] -for lengths in l: - params.append(lengths) - -for masses in m: - params.append(masses) - -for masses in M: - params.append(masses) - -for inertias in Ixx: - params.append(inertias) - -for inertias in Iyy: - params.append(inertias) - -for inertias in Izz: - params.append(inertias) -params.append(g) - -print params - -right_hand_side = numeric_right_hand_side(kane, params) - -param_vals = [10, 10, 10, 5, 5, 5, 10, 10, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 9.8] -t = [i*1 for i in range(0,10)] #Taking 10 time intervals of 0.1 sec -x0 = [45,45,45,45,45,45,0,0,0,0,0,0] -numeric_vals = odeint(right_hand_side, x0, t, args=(param_vals,)) -print numeric_vals - From 5a79f75d28003c9471da0d5956b01c9b02c849ab Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Fri, 12 Jul 2013 17:16:20 +0530 Subject: [PATCH 10/33] [WIP] Python part nearly complete, some problems with json serialization --- illustrative_example_for_viz/essential.py | 45 +- .../illustrative_example.py | 15 +- illustrative_example_for_viz/output | 901 ++++++++++++++++++ 3 files changed, 945 insertions(+), 16 deletions(-) create mode 100644 illustrative_example_for_viz/output diff --git a/illustrative_example_for_viz/essential.py b/illustrative_example_for_viz/essential.py index fa2aa69..7905a0c 100644 --- a/illustrative_example_for_viz/essential.py +++ b/illustrative_example_for_viz/essential.py @@ -43,7 +43,13 @@ def origin(self): @color.setter def origin(self, new_origin): self._origin = new_origin - + + def generate_data(self): + self._data = {} + self._data['name'] = self.name + self._data['points'] = self.points + self._data['color'] = self.color + return self._data class VisualizationFrame(object): def __init__(self, name, rigidbody, shape=None): @@ -77,27 +83,52 @@ def generate_simulation_data(self,values_list,timesteps=None): for iterator in range(0,timesteps): self.simulation_matrix.append(self._transform.evalf(subs=values_list[iterator])) return self.simulation_matrix + + def generate_simulation_dict(self): + self._data = {} + self._data['name'] = self._name + + self._data['shape'] = {} + + self._data['shape'] = self._shape.generate_data() #hidden method + self._data['simulation_matrix'] = self.simulation_matrix + return self._data class Scene(): def __init__(self,name,reference_frame,origin,height=800,width=800): self._name = name self._reference_frame=reference_frame self._origin = origin #contains point - self._child_vframes = [] + self._child_frames = [] self._height = height self._width = width def add_visualization_frames(self,vframes): for _vframe in vframes: - self._child_vframes.append(_vframe) + self._child_frames.append(_vframe) def add_visualization_frame(self,vframe): - self._child_vframes.append(vframe) + self._child_frames.append(vframe) - def generate_json(self): + def generate_json(self,values_list,timesteps=None): + + self._scene_data = {} + self._scene_data['name'] = self._name + self._scene_data['height'] = self._height + self._scene_data['width'] = self._width + self._scene_data['frames'] = {} - #TODO - pass + for frame in self._child_frames[0]: + + frame.transform(self._reference_frame,self._origin) + frame.generate_simulation_data(values_list,timesteps=100) + self._scene_data['frames'][frame.__str__()] = frame.generate_simulation_dict() + + return self._scene_data + + + + diff --git a/illustrative_example_for_viz/illustrative_example.py b/illustrative_example_for_viz/illustrative_example.py index 178e2a6..f8be28a 100644 --- a/illustrative_example_for_viz/illustrative_example.py +++ b/illustrative_example_for_viz/illustrative_example.py @@ -3,6 +3,7 @@ from essential import * from simulate import * +import json #setting some shapes for the pendulums .. shape1 = MeshShape('shape1',[[1,1,1], [0,1,1], [2,1,1]], \ @@ -17,20 +18,16 @@ #Setting up some vframes ... frame1 = VisualizationFrame('frame1', link1, shape=shape1) - -#Now these methods would be called from within Scene for generating -#simulation data, similar for all frames -frame1.transform(I,O) -simulation_matrix1 = frame1.generate_simulation_data(values_list,timesteps=100) -print simulation_matrix1 - - frame2 = VisualizationFrame('frame2', link2, shape=shape2) frame3 = VisualizationFrame('frame3', link3, shape=shape3) scene = Scene('scene1',I,O) scene.add_visualization_frame([frame1,frame2,frame3]) -scene.generate_json() +data = scene.generate_json(values_list,timesteps=100) +print data +f = open('output','w') +f.write(str(data)) + diff --git a/illustrative_example_for_viz/output b/illustrative_example_for_viz/output new file mode 100644 index 0000000..3a4310b --- /dev/null +++ b/illustrative_example_for_viz/output @@ -0,0 +1,901 @@ +{'frames': {'': {'shape': {'color': 'blue', 'points': [[1, 1, 1], [0, 1, 1], [2, 1, 1]], 'name': 'shape2'}, 'name': 'frame2', 'simulation_matrix': [[ 0.984807753012208, 0.17364817766693, 0, -0.855050358314172] +[-0.171010071662834, 0.969846310392954, 0.17364817766693, 4.84923155196477] +[0.0301536896070458, -0.171010071662834, 0.984807753012208, 0.868240888334652] +[ 0, 0, 0, 1.0], [ 0.98476856287105, 0.173870289528966, 0, -0.856142872387446] +[-0.171228574477489, 0.96980638651645, 0.173655831904124, 4.84903193258225] +[0.0301935897715636, -0.171010804018401, 0.984806403333004, 0.868279159520621] +[ 0, 0, 0, 1.0], [ 0.984486567312166, 0.175459963472892, 0, -0.863953961989447] +[-0.172790792397889, 0.969510141823486, 0.173762559154481, 4.84755070911743] 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1.0], [ 1.0, 7.05390644685064e-71, 0, -3.52695322342532e-70] +[-7.05390644685064e-71, 1.0, 7.3468340141945e-250, 5.0] +[5.18238798166682e-320, -7.3468340141945e-250, 1.0, 3.67341700709725e-249] +[ 0, 0, 0, 1.0], [ 1.0, 2.86407800464107e-110, 0, -1.43203900232054e-109] +[-2.86407800464107e-110, 1.0, 7.34734550155944e-250, 5.0] +[ 2.10433706435149e-359, -7.34734550155944e-250, 1.0, 3.67367275077972e-249] +[ 0, 0, 0, 1.0]]}}, 'width': 800, 'name': 'scene1', 'height': 800} \ No newline at end of file From 134bf8880fc342c5eb1000276175ddb1427fa5fc Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Fri, 12 Jul 2013 17:51:43 +0530 Subject: [PATCH 11/33] WIP --- illustrative_example_for_viz/essential.py | 9 +- .../illustrative_example.py | 4 +- illustrative_example_for_viz/output | 902 +----------------- 3 files changed, 10 insertions(+), 905 deletions(-) diff --git a/illustrative_example_for_viz/essential.py b/illustrative_example_for_viz/essential.py index 7905a0c..538007b 100644 --- a/illustrative_example_for_viz/essential.py +++ b/illustrative_example_for_viz/essential.py @@ -81,7 +81,12 @@ def eval_transform(self): def generate_simulation_data(self,values_list,timesteps=None): self.simulation_matrix = [] for iterator in range(0,timesteps): - self.simulation_matrix.append(self._transform.evalf(subs=values_list[iterator])) + self.simulation_matrix.append(self._transform.evalf(subs=values_list[iterator]).tolist()) + temp = self._transform.evalf(subs=values_list[iterator]) + + print temp + print type(temp) + print type(self.simulation_matrix) return self.simulation_matrix def generate_simulation_dict(self): @@ -124,7 +129,7 @@ def generate_json(self,values_list,timesteps=None): frame.transform(self._reference_frame,self._origin) frame.generate_simulation_data(values_list,timesteps=100) - self._scene_data['frames'][frame.__str__()] = frame.generate_simulation_dict() + self._scene_data['frames'][frame._name] = frame.generate_simulation_dict() return self._scene_data diff --git a/illustrative_example_for_viz/illustrative_example.py b/illustrative_example_for_viz/illustrative_example.py index f8be28a..176b09d 100644 --- a/illustrative_example_for_viz/illustrative_example.py +++ b/illustrative_example_for_viz/illustrative_example.py @@ -25,9 +25,9 @@ scene = Scene('scene1',I,O) scene.add_visualization_frame([frame1,frame2,frame3]) data = scene.generate_json(values_list,timesteps=100) -print data f = open('output','w') f.write(str(data)) - +f = open('output1','w') +f.write(json.dumps(data)) diff --git a/illustrative_example_for_viz/output b/illustrative_example_for_viz/output index 3a4310b..273364c 100644 --- a/illustrative_example_for_viz/output +++ b/illustrative_example_for_viz/output @@ -1,901 +1 @@ -{'frames': {'': {'shape': {'color': 'blue', 'points': [[1, 1, 1], [0, 1, 1], [2, 1, 1]], 'name': 'shape2'}, 'name': 'frame2', 'simulation_matrix': [[ 0.984807753012208, 0.17364817766693, 0, -0.855050358314172] -[-0.171010071662834, 0.969846310392954, 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'name': 'scene1', 'height': 800} \ No newline at end of file From f769203de5a2e92d15e8b704dc79263b60417bd1 Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Sat, 13 Jul 2013 13:13:09 +0530 Subject: [PATCH 12/33] [WIP] Completed Python side, although in a dirty way, with some hacks --- illustrative_example_for_viz/essential.py | 30 +++++----- .../illustrative_example.py | 11 ++-- illustrative_example_for_viz/output | 1 - illustrative_example_for_viz/output.json | 1 + .../pendulum_simulation.ipynb | 58 +++++++++++++++++++ illustrative_example_for_viz/simulate.py | 18 +++--- .../three_link_pendulum.py | 47 ++++++--------- 7 files changed, 109 insertions(+), 57 deletions(-) delete mode 100644 illustrative_example_for_viz/output create mode 100644 illustrative_example_for_viz/output.json create mode 100644 illustrative_example_for_viz/pendulum_simulation.ipynb diff --git a/illustrative_example_for_viz/essential.py b/illustrative_example_for_viz/essential.py index 538007b..5b1d6a6 100644 --- a/illustrative_example_for_viz/essential.py +++ b/illustrative_example_for_viz/essential.py @@ -4,6 +4,7 @@ #also it doesnot check for TypeErrors etc. import numpy as np from sympy.matrices.expressions import Identity +from sympy import lambdify class MeshShape(object): def __init__(self, name, point_list, color='grey', origin=[0,0,0]): @@ -74,19 +75,22 @@ def transform(self, reference_frame, point): return self._transform - def eval_transform(self): - self._numerical_transform = self._transform.evalf(subs=vel_dict) - return self._numerical_transform - - def generate_simulation_data(self,values_list,timesteps=None): + def generate_simulation_data(self,values_list): self.simulation_matrix = [] - for iterator in range(0,timesteps): - self.simulation_matrix.append(self._transform.evalf(subs=values_list[iterator]).tolist()) - temp = self._transform.evalf(subs=values_list[iterator]) + for vals in values_list: + evaluated = self._transform.evalf(subs=vals).tolist() + temp_list = [] + for vals in evaluated: + temp_list1 = [] + for val1 in vals: + temp_list1.append(float(val1)) + temp_list.append(temp_list1) + + print 'evaluated = %s \n'%evaluated + + self.simulation_matrix.append(temp_list) + - print temp - print type(temp) - print type(self.simulation_matrix) return self.simulation_matrix def generate_simulation_dict(self): @@ -117,7 +121,7 @@ def add_visualization_frame(self,vframe): self._child_frames.append(vframe) - def generate_json(self,values_list,timesteps=None): + def generate_json(self,values_list): self._scene_data = {} self._scene_data['name'] = self._name @@ -128,7 +132,7 @@ def generate_json(self,values_list,timesteps=None): for frame in self._child_frames[0]: frame.transform(self._reference_frame,self._origin) - frame.generate_simulation_data(values_list,timesteps=100) + frame.generate_simulation_data(values_list) self._scene_data['frames'][frame._name] = frame.generate_simulation_dict() return self._scene_data diff --git a/illustrative_example_for_viz/illustrative_example.py b/illustrative_example_for_viz/illustrative_example.py index 176b09d..89ee87a 100644 --- a/illustrative_example_for_viz/illustrative_example.py +++ b/illustrative_example_for_viz/illustrative_example.py @@ -24,10 +24,11 @@ scene = Scene('scene1',I,O) scene.add_visualization_frame([frame1,frame2,frame3]) -data = scene.generate_json(values_list,timesteps=100) -f = open('output','w') -f.write(str(data)) -f = open('output1','w') -f.write(json.dumps(data)) + +dynamic_params = alpha + beta + omega + delta +data = scene.generate_json(values_list) + +f = open('output.json','w') +f.write('var JSONObj=' + json.dumps(data) + ';') diff --git a/illustrative_example_for_viz/output b/illustrative_example_for_viz/output deleted file mode 100644 index 273364c..0000000 --- a/illustrative_example_for_viz/output +++ /dev/null @@ -1 +0,0 @@ -{'frames': {'frame3': {'shape': {'color': 'green', 'points': [[1, 1, 1], [0, 1, 1], [2, 1, 1]], 'name': 'shape3'}, 'name': 'frame3', 'simulation_matrix': [[[0.984807753012208, 0.173648177666930, 0, -0.855050358314172], [-0.171010071662834, 0.969846310392954, 0.173648177666930, 4.84923155196477], [0.0301536896070458, -0.171010071662834, 0.984807753012208, 0.868240888334652], [0, 0, 0, 1.00000000000000]], [[0.984807680117067, 0.173648591075311, 0, -0.855052392164692], [-0.171010478432938, 0.969846236576786, 0.173648189348414, 4.84923118288393], [0.0301537634231310, -0.171010070508741, 0.984807750952447, 0.868240946742072], [0, 0, 0, 1.00000000000000]], [[0.984805411677293, 0.173661455513642, 0, -0.855115640799528], [-0.171023128159906, 0.969843893313584, 0.173648818702432, 4.84921946656792], [0.0301561066040889, -0.171010296389524, 0.984807639980138, 0.868244093512160], [0, 0, 0, 1.00000000000000]], [[0.984789946601407, 0.173749132581428, 0, -0.855546428788729], [-0.171109285757746, 0.969827600753082, 0.173654937001501, 4.84913800376541], [0.0301723946724934, -0.171013636136779, 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"metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "display(HTML(\"\"\"\n", + " \n", + " \"\"\"))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + " \n", + " " + ], + "output_type": "display_data", + "text": [ + "" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/illustrative_example_for_viz/simulate.py b/illustrative_example_for_viz/simulate.py index 9af669f..1f3d505 100644 --- a/illustrative_example_for_viz/simulate.py +++ b/illustrative_example_for_viz/simulate.py @@ -35,22 +35,22 @@ params.append(g) param_vals.append(9.8) + print params print param_vals right_hand_side = numeric_right_hand_side(kane, params) -t = [i*0.1 for i in range(0,100)] #Taking 10 time intervals of 0.1 sec +t = [i*0.1 for i in range(0,10)] #Taking 10 time intervals of 0.1 sec x0 = [radians(10), radians(10), radians(10), radians(10), radians(10), \ - radians(10), radians(10), 0, 0, 0, 0, 0] - -numeric_vals = odeint(right_hand_side, x0, t, args=(param_vals,)) + radians(10), 0, 0, 0, 0, 0, 0] +numerical_vals = odeint(right_hand_side, x0, t, args=(param_vals,)) +#saving numerical vals as a dict: -#mapping in a dict: values_list = [] -for val in numeric_vals: +for val in numerical_vals: val_dict = {} val_dict[alpha[0]] = val[0] val_dict[alpha[1]] = val[1] @@ -58,10 +58,12 @@ val_dict[beta[0]] = val[3] val_dict[beta[1]] = val[4] val_dict[beta[2]] = val[5] - #Since lengths are also used in defining some positions ... + + #lengths are also required in dict + val_dict[l[0]] = 10 val_dict[l[1]] = 10 val_dict[l[2]] = 10 values_list.append(val_dict) -print values_list[0] +print values_list diff --git a/illustrative_example_for_viz/three_link_pendulum.py b/illustrative_example_for_viz/three_link_pendulum.py index 4fb3ce3..0032a29 100644 --- a/illustrative_example_for_viz/three_link_pendulum.py +++ b/illustrative_example_for_viz/three_link_pendulum.py @@ -43,11 +43,11 @@ #And some other frames ... A = ReferenceFrame('A') -A.orient(I,'Body',[alpha[0],beta[0],0],'ZXY') +A.orient(I,'Space',[alpha[0],beta[0],0],'ZXY') B = ReferenceFrame('B') -B.orient(I,'Body',[alpha[1],beta[1],0],'ZXY') +B.orient(I,'Space',[alpha[1],beta[1],0],'ZXY') C = ReferenceFrame('C') -C.orient(I,'Body',[alpha[2],beta[2],0],'ZXY') +C.orient(I,'Space',[alpha[2],beta[2],0],'ZXY') #Setting angular velocities of new frames ... @@ -70,12 +70,12 @@ P1.v2pt_theory(O, I, A) P2.v2pt_theory(P1, I, B) P3.v2pt_theory(P2, I, C) -points = [P1,P2,P3] +points = [P1, P2, P3] Pa1 = Particle('Pa1', points[0], m[0]) Pa2 = Particle('Pa2', points[1], m[1]) Pa3 = Particle('Pa3', points[2], m[2]) -particles = [Pa1,Pa2,Pa3] +particles = [Pa1, Pa2, Pa3] @@ -89,21 +89,21 @@ P_link2.v2pt_theory(P_link1, I, B) P_link3.v2pt_theory(P_link2, I, C) -points_rigid_body = [P_link1,P_link2,P_link3] +points_rigid_body = [P_link1, P_link2, P_link3] #defining inertia tensors for links -inertia_link1 = inertia(A,Ixx[0],Iyy[0],Izz[0]) -inertia_link2 = inertia(B,Ixx[1],Iyy[1],Izz[1]) -inertia_link3 = inertia(C,Ixx[2],Iyy[2],Izz[2]) +inertia_link1 = inertia(A, Ixx[0], Iyy[0], Izz[0]) +inertia_link2 = inertia(B, Ixx[1], Iyy[1], Izz[1]) +inertia_link3 = inertia(C, Ixx[2], Iyy[2], Izz[2]) #Defining links as Rigid bodies ... -link1 = RigidBody('link1', P_link1, A, M[0], (inertia_link1, O)) -link2 = RigidBody('link2', P_link2, B, M[1], (inertia_link2, P1)) -link3 = RigidBody('link3', P_link3, C, M[2], (inertia_link3, P2)) -links = [link1,link2,link3] +link1 = RigidBody('link1', P_link1, A, M[0], (inertia_link1, P_link1)) +link2 = RigidBody('link2', P_link2, B, M[1], (inertia_link2, P_link2)) +link3 = RigidBody('link3', P_link3, C, M[2], (inertia_link3, P_link3)) +links = [link1, link2, link3] #Applying forces on all particles , and adding all forces in a list.. @@ -119,31 +119,18 @@ mass = link.get_mass() point = link.get_masscenter() forces.append((point, -mass * g * I.y) ) + kinematic_differentials = [] for i in range(0,N_bobs): kinematic_differentials.append(omega[i] - alpha[i].diff(t)) kinematic_differentials.append(delta[i] - beta[i].diff(t)) #Adding particles and links in the same system ... -total_system = [] -for particle in particles: - total_system.append(particle) - -for link in links: - total_system.append(link) - -q = [] -for angle in alpha: - q.append(angle) -for angle in beta: - q.append(angle) +total_system = links + particles -u = [] -for vel in omega: - u.append(vel) -for vel in delta: - u.append(vel) +q = alpha + beta +u = omega + delta kane = KanesMethod(I, q_ind=q, u_ind=u, kd_eqs=kinematic_differentials) fr, frstar = kane.kanes_equations(forces, total_system) From 31e7b655553d8f575b8cf4fa104abb3e28182d7b Mon Sep 17 00:00:00 2001 From: Tarun Gaba Date: Sun, 14 Jul 2013 12:58:34 +0530 Subject: [PATCH 13/33] WIP Added some javascript code --- illustrative_example_for_viz/essential.py | 3 +- .../illustrative_example.py | 2 +- illustrative_example_for_viz/js/Canvas.js | 101 +++ illustrative_example_for_viz/js/libs/LICENCE | 21 + .../js/libs/TrackballControls.js | 537 +++++++++++++ .../js/libs/three.min.js | 710 ++++++++++++++++++ illustrative_example_for_viz/js/main.js | 141 ++++ illustrative_example_for_viz/js/output.json | 1 + .../pendulum_simulation.ipynb | 138 +++- mass_spring/viz.py | 2 + 10 files changed, 1647 insertions(+), 9 deletions(-) create mode 100644 illustrative_example_for_viz/js/Canvas.js create mode 100644 illustrative_example_for_viz/js/libs/LICENCE create mode 100644 illustrative_example_for_viz/js/libs/TrackballControls.js create mode 100644 illustrative_example_for_viz/js/libs/three.min.js create mode 100644 illustrative_example_for_viz/js/main.js create mode 100644 illustrative_example_for_viz/js/output.json diff --git a/illustrative_example_for_viz/essential.py b/illustrative_example_for_viz/essential.py index 5b1d6a6..5dcd0f0 100644 --- a/illustrative_example_for_viz/essential.py +++ b/illustrative_example_for_viz/essential.py @@ -46,7 +46,8 @@ def origin(self, new_origin): self._origin = new_origin def generate_data(self): - self._data = {} + self._data = {} + self._data['type'] = 'Mesh' self._data['name'] = self.name self._data['points'] = self.points self._data['color'] = self.color diff --git a/illustrative_example_for_viz/illustrative_example.py b/illustrative_example_for_viz/illustrative_example.py index 89ee87a..a48a534 100644 --- a/illustrative_example_for_viz/illustrative_example.py +++ b/illustrative_example_for_viz/illustrative_example.py @@ -29,6 +29,6 @@ dynamic_params = alpha + beta + omega + delta data = scene.generate_json(values_list) -f = open('output.json','w') +f = open('js/output.json','w') f.write('var JSONObj=' + json.dumps(data) + ';') diff --git a/illustrative_example_for_viz/js/Canvas.js b/illustrative_example_for_viz/js/Canvas.js new file mode 100644 index 0000000..98e5637 --- /dev/null +++ b/illustrative_example_for_viz/js/Canvas.js @@ -0,0 +1,101 @@ +//THis file basically creates a Canvas class like object. +container.show(); + +function Canvas(JSONObj) +{ + + this.visualization_frames = JSONObj.frames; + this.width = JSONObj.width; + this.height = JSONObj.height; + + this.initialize = function (){ + // This function initializes a simple Canvas, with mouse controls + + // first of all , a renderer ... + this.renderer = new THREE.WebGLRenderer(); + + //show the IPython handle container + container.show(); + + // create a canvas div + this.canvas = $("
").attr("id", "#canvas"); + this.canvas.attr("style","background-color:rgb(104,104,104)"); + + // Now lets add a scene .. + + this.scene = new THREE.Scene(); + + // A Camera .. + var VIEW_ANGLE = 45, + ASPECT = WIDTH / HEIGHT, + NEAR = 0.1, + FAR = 1000; + + this.camera = new THREE.PerspectiveCamera( VIEW_ANGLE, + ASPECT, + NEAR, + FAR ); + + // the camera starts at 0,0,0 so pull it back + this.camera.position.z = 10; + + // Add trackball controls ... + + this.controls = new THREE.TrackballControls(camera, renderer.domElement); + + this.reset = function(){ controls.reset();} + + this.scene.add(this.camera); + + this.reset_button = $('