# How to calculate required torque for a robot arm

• meakerb
meakerb
TL;DR Summary
I am trying to size the two motors needed for a robot arm I'm building. The pivot point for one motor is (through two pulleys) at the end of an arm driven by another motor.
I am trying to size the two motors needed for a robot arm I'm building.
The first motor, which I call the wrist motor, drives a pulley on a fixed axis that connects to a second pulley (of the same size) which is attached to a hand and load.

I can calculate the moment of inertia for the hand and load about the axis of the second pulley, and therefore calculate the required torque for the wrist motor.

However, the second motor, which I call the shoulder motor, also rotates on the same fixed axis as the wrist motor, but it rotates an arm that holds the second pulley.

The first diagram, and my calculation for required torque for the wrist motor, assumed the shoulder motor was fixed (thereby fixing the axis of pulley 2). To calculate the required torque of the shoulder motor, do I assume that the wrist motor is fixed and use the parallel axis theroem for the moi of the hand & load, plus the moi of the arm? This doesn't seem right to me since, if the wrist motor is fixed, the gearing effect of the two pulleys will keep the hand & load at the same relative angle to the ground.

In reality, both motors will be moving at the same time. Any insight is greatly appreciated.

You have a motor bolted to a motor. If we imagine holding the shoulder motor still while rotating the wrist motor its clear that that any torque that is developed in the wrist motor, must be resisted by the shoulder motor. So...what happens when we start simultaneously rotating the shoulder motor. It seems clear to me that the shoulder motor (isolated from the system) has torque acting on it that depends on what the wrist motor is doing. How it all shakes out seems complicated at the moment.

I think we should start with a FBD of the blue arm at the end.

berkeman
meakerb said:
I am trying to size the two motors needed for a robot arm I'm building.

meakerb said:
Any insight is greatly appreciated.
Since this is an engineering, as opposed to a physics problem, we need only find the worst case torque for each motor. That will be the case where:

The arm is horizontal
and
The hand is horizontal
and
The hand is holding the heaviest load with the center of gravity (CG) farthest out
and
The hand is accelerating clockwise at maximum ##radians/sec^2##
and
The arm is accelerating clockwise at maximum ##radians/sec^2##

There is more than one way to solve this. This is how I would attack the problem.

1) Given the maximum acceleration of the arm, calculate the vertical acceleration of the wrist joint in ##inches/sec^2##
2) The torque at the wrist will be the value you calculated PLUS the vertical acceleration of the arm at the wrist times the distance to the hand/load CG times the mass of the hand/load. This is the required peak torque of the wrist motor.
3) Pretend that the wrist is locked in a straight line with the arm. Calculate the arm torque at maximum arm acceleration for that case. This calculation uses the total mass of the arm, hand, and load.
4) The peak torque requirement for the arm motor is the sum of the torques calculated in Steps 2 and 3.
5) The peak RPM of the arm motor is merely the maximum arm angular velocity.
6) The peak RPM of the wrist motor is calculated from the maximum hand angular velocity when the arm is moving at maximum angular velocity in the opposite direction.

This problem will benefit from careful step by step note taking. Diagrams are good.

## 1. What factors do I need to consider when calculating the required torque for a robot arm?

When calculating the required torque for a robot arm, you need to consider the mass of the arm and the payload, the length of each arm segment, the acceleration due to gravity, the angular acceleration, and any friction or resistance in the joints. Each of these factors will influence the amount of torque needed to move the arm efficiently and accurately.

## 2. How do I calculate the torque needed for each joint of a robot arm?

To calculate the torque needed for each joint, you can use the formula: Torque (τ) = Force (F) x Distance (r). For a robot arm, the force is typically the weight of the arm segment and its payload, and the distance is the length of the arm segment from the joint to the center of mass. You also need to account for the angular acceleration and any additional forces due to movement or external loads.

## 3. What is the role of the center of mass in torque calculations for a robot arm?

The center of mass is crucial in torque calculations because it determines the point where the mass of the arm segment and payload can be considered to act. The distance from the joint to the center of mass is used in the torque formula to calculate the rotational force needed. Accurately locating the center of mass helps in determining the correct torque required to move the arm efficiently.

## 4. How does angular acceleration affect the torque required for a robot arm?

Angular acceleration affects the torque required because it represents the rate of change of angular velocity. According to Newton's second law for rotation, Torque (τ) = Moment of Inertia (I) x Angular Acceleration (α). Higher angular acceleration requires more torque to achieve the desired movement. This is especially important in applications requiring rapid or precise movements.

## 5. Can software tools help in calculating the required torque for a robot arm?

Yes, software tools can significantly aid in calculating the required torque for a robot arm. CAD software and specialized robotic simulation tools can model the robot arm's dynamics, including the mass, center of mass, and forces involved. These tools can run simulations to provide accurate torque requirements for each joint under various operating conditions, saving time and reducing the risk of errors in manual calculations.

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