# How to Calculate Torque on a Robot Arm

Written by pauline gill
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Torque is an expression of twisting force around an axis. Units used to communicate torque describe both the size of the tangential force, and the length of the arm applying the force to the shaft. For example, a 100-pound weight hanging at the end of a one-foot arm with its other end mounted on a shaft would apply 100-foot-pounds of torque to the shaft. It is possible to calculate the torque of a robot arm either by analysing the load forces or the motor forces trying to rotate the arm holding the load.

Skill level:
Moderate

### Things you need

• Calculator or spreadsheet

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## Load-Based Calculations

1. 1

Define the load. For example, if you lift a 250-pound machine with a 4-foot long robot arm until the arm is exactly horizontal, all of the downward force from gravity, 113 Kilogram, will be translated into torque at the motor shaft supporting the arm.

2. 2

Define the moment-arm. The arm is effectively 4 feet long when it is horizontal, since gravity is applied perpendicularly to it.

3. 3

Multiply the load in pounds by the effective length of the arm in feet to obtain the torque in foot-pounds. 113 Kilogram multiplied by 4 feet equals 1000 foot-pounds of torque from the machine's weight.

4. 4

Add any weight as a result of the robot arm's weight. If the robot arm itself weighs 45.4 Kilogram, and the arm is uniform, its centre of gravity can be considered to be at the middle of the arm, which is 2 feet from the shaft in our example. The moment arm for robot arm weight can be considered to be 2 feet. Multiply 45.4 Kilogram by 2 feet to obtain the additional torque on the robot arm of 200 foot-pounds.

5. 5

Add 1000 foot-pounds to 200 foot-pounds as a result of the machine and the arm respectively, to obtain a total torque on the robot arm of 1200 foot-pounds.

6. 6

Convert to other engineering units as necessary. Multiply foot-pounds by 12 inches-per-foot to obtain in-pounds, and further by 16 to obtain inch-ounces. The 1200 foot-pound torque on the example here would be 230,400 inch-ounces (or ounce-inches). Multiply foot-pounds by 1.356 to obtain 1627.2 Newton-meters (Nm), the primary metric unit of torque.

## Motor-Based Calculations

1. 1

Use desired robotic arm torque and lift speed to determine the motor torque and horsepower. If the example lift speed is 10 feet-per-minute, then it is possible to specify motor torque and horsepower. The 4-foot robot arm circle has a circumference of 25.13 feet. Ten feet-per-minute divided by 25.13 feet would yield a revolutions-per-minute (rpm) figure of about 0.4rpm.

2. 2

Calculate the required horsepower by applying the motor formula HP=Torque x rpm/5252. The calculation would be 1200 foot-pounds x .4/5252 or 0.09 horsepower. Designers usually double or triple this figure as a safety to specify a motor, since an electric motor will only draw the power needed to lift the load.

3. 3

Calculate delivered robot arm torque by measuring energy applied. If the motor uses electricity at the rate of 67 watt/hours to lift the example weight, multiply by 746 watts-per-horsepower to arrive at 0.09 horsepower generated to lift the weight and arm. This would yield 5252 x 0.09/rpm or a required robot arm torque of 1200 foot-pounds.

#### Tips and warnings

• Design conservatively when robot arms continually lift heavy weights.
• Robotics can turn or suddenly release objects without warning. Always observe safe zone markings on plant floors to prevent injury.

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