🤖 Robotic Arm Torque & Servo Selection analysis

task Description

This task involves evaluating a robotic arm with three joints (three servo motors) designed to carry a 1 kg payload. Our objectives are:

Task 1:

1. Calculate the torque required at each joint (for 1 kg payload).
2. Recommend the best and most appropriate servo motor for each joint.

Task 2:

3. Evaluate: Can the same motors (selected for 1 kg) lift 2 kg if we add gears?
4. Analyze the specific drawbacks we would face in that 2 kg case.
5. Propose engineering alternatives to overcome those specific drawbacks.

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Robotic Arm Measurements

Segment	Length (cm)	Length (m)
L1	15	0.15
L2	10	0.10
L3	4	0.04

Total Arm Reach from base to payload: 0.29 m
Payload: 1 kg
Gravity (g): 9.81 m/s²

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Torque Calculations — for 1 KG Payload

Force = Mass × Gravity = 1 × 9.81 = 9.81 N

Joint 3 (Wrist)

• Load distance from joint: 0.04 m
• Torque = 9.81 × 0.04 = 0.39 Nm
• With 1.5× safety margin = 0.59 Nm

Joint 2 (Elbow)

• Load is 1 kg at 0.04 m + arm L3 (0.04 m from J2)
• Total distance = 0.04 m
• Torque = 9.81 × 0.04 = 0.39 Nm
• With 1.5× safety margin = 0.59 Nm

Joint 1 (Base)

• Load at total reach (L2 + L3) = 0.10 + 0.04 = 0.14 m
• Torque = 9.81 × 0.14 = 1.37 Nm
• With 1.5× safety margin = 2.06 Nm

Joint	Load Distance	Torque (Nm)	With Safety Margin
J3 (Wrist)	0.04 m	0.39 Nm	0.59 Nm
J2 (Elbow)	0.04 m	0.39 Nm	0.59 Nm
J1 (Base)	0.14 m	1.37 Nm	2.06 Nm

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Recommended Servo Motors (For 1 KG)

Joint	Torque Needed	Servo Recommendation	Rated Torque	Status
J1	2.06 Nm	MG996R or Dynamixel AX-18A	~3–4 Nm	Safe
J2	0.59 Nm	MG90S or MG996R	~2–3 Nm	Overkill
J3	0.59 Nm	SG90 or MG90S	~1–2 Nm	Suitable

These motors are selected assuming no gear ratios are used and based on the 1 kg payload scenario only.

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TASK 2: Can the Same Motors Carry 2 KG With Gears?

New Load: 2 KG

Force = 2 × 9.81 = 19.62 N

Joint	Load Point	Required Torque (Nm)	Gear Ratio Needed (approx)
J3	0.04 m	0.78 Nm	0.78 / 1.0 = ~0.8×
J2	0.04 m	0.78 Nm	0.78 / 2.0 = ~0.4×
J1	0.14 m	2.75 Nm	2.75 / 3.0 = ~0.92×

So: Yes, the same motors can carry 2 KG if modest gear ratios (1.1×–1.3×) are added where needed.

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⚠️ Specific Cons of Using Gears to Lift 2 KG

Problem	Why It Happens (with 2kg)
Overheating	Motors work harder, gear friction adds heat
Slow Movement	Gear reduction sacrifices speed for torque
Inaccuracy	Gears introduce backlash — wobble and lag
Current Drain	More torque → higher current = faster battery depletion
Mechanical Stress	Heavier system and gear forces stress shafts and mounts
Maintenance Need	More moving parts = higher chance of mechanical failure

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Engineering Alternatives to Gearing

Method	What It Solves
Use Higher Torque Servos	Avoids need for gearing, less stress on components
Add Counterweights	Balances torque, reducing motor strain
Use Lightweight Materials	Reduces overall required torque
Redesign Arm Geometry	Keeps center of mass closer to base
Stepper Motors + Drivers	Provide higher torque + precision without servo lag
Harmonic Drives	Compact gear solution without backlash
Limit Payload to 1.5 kg	Stays within safe operating range of motors

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Conclusion

• For 1 kg payload, the updated torque values based on correct arm geometry confirm smaller servos are sufficient.
• For 2 kg, using minor gears or upgrading motor specs is necessary.
• Gearing adds drawbacks like heat, slow response, and wear.
• Preferred solutions: stronger motors, smarter geometry, or harmonic drives.

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