# Gym exercise equipment analysis

1. Jul 24, 2015

### JasmineRM

I need some help on the direction to go with this problem. This is a workarm on a leg extension machine and there's 300 pounds (max) coming from the weight stack attached via a cable on the cam. I need to find the total force exterted on this system to double check my results on an analysis.

To explain the diagram a littler more, there's a cam that exerts a torque onto the shaft connected to it. Then there's a perpendicular lever connected to that where the leg extension pad is connected perpendicular to that. I know there's a force exerted on to the work arm from a person seated using the machine.

I know for sure I can calculate the torque on the cam using distances from the cable as different degrees to the pivot point and multiplying that by the 300 lbs. I am lost on how to approach the rest. Should I analyze part by part or as a whole system? Any input would be great because I've racked my head on this for quite some time and I am stuck. Thank you

2. Jul 24, 2015

### lightgrav

Are you trying to find the Force by the user's leg (as a function of angle), or the reaction Forces applied to the shaft by the bearings?
that is, are you analyzing the biology/kinesiology, or the mechanical machine structure?

3. Jul 24, 2015

### JasmineRM

The mechanical machine structure

4. Jul 28, 2015

### JasmineRM

Would this be the correct thinking....
I analyzed each part separately. For the cam, I took the distance from the cable to the center and found the max torque to be 2435.4 lb*in. Then for the rotating bearing, I used T = F*d, with the force being 300 lb and distance as the length of the bearing, getting 1912.5 lb*in. For the lever, I used the cantilever beam equation and 3750 lb*in. As for the final beam which is where the leg has a force going up on ...I was unsure of how to go about the forces on this one. I have two reaction forces, one in the x and one in the y which equals 300lb, weight going down, another weight of a person going down because there's a potential someone could sit in the end of this beam (although hopefully unlikely) that is at max 300 lb(weight stack weight), and the questionable force going up that I am trying to find.

Is this correct?

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