# Sizing Linear Actuator to Rotate a Shaft

I have a horizontal arm attached to a shaft that I have calculated to require 151 in-lbs of torque. I would like to calculate the force required of a linear actuator to rotate the shaft via a 3.5" linkage. Is it as simple as converting the torque to a linear force at 3.5" (Force = Torque/ Distance)? This gives me a force of 42.8 lbs. Thanks!

• What you have is no different than a balancing lever with the fulcrum off center. The short arm is one side of the lever, the long arm is the other. The only difference is that the lever is bent at the fulcrum and not straight. You can use torque to transfer calculations from one arm to the other, or directly use the ratio of lever arm lengths. Jun 23 at 0:35
• You're almost right. The actuator will not be pushing on the short arm at a perfect right angle at all times, so you'll have to check the angle and force requirements throughout the stroke.
– Drew
Jun 23 at 0:55
• Just wondering... what angle do you want the driven arm to swing? Jun 23 at 3:19
• Is there a reason you don't want to use a rotary actuator?
– jko
Jun 23 at 11:32

## intro to force moments

Assuming that the actuator is fixed at one point and its allowed to rotate you can imagine that the following two cases will have completely different torque moments (the one to the right it will be zero). The reason is that the torque is given by $$T = \vec{r}\times \vec{F}$$

or

$$T = |r|\cdot |F|\sin\theta$$

where $$\theta$$ is the angle between the radius and the vector of force. Figure 1: Angle $$\theta$$ when the actuator is closing (pulling downwards)

## how to size the force

In order to properly dimension/size the system, apart from the maximum moment you need to know the following:

• range of movement of the linkage in degrees (if the range of movement for the linkage is small then everything is much simpler).

• calculate the maximum bending moment at each position of the linkage (in the best scenario, only one position has the highest value).

• position and support of the actuator

Only if you have those, then its possible to do a proper dimensioning of the force.

As a final note, please take note at jko's comment underneath your question.

Is there a reason you don't want to use a rotary actuator?