Gym exercise equipment analysis

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Discussion Overview

The discussion revolves around analyzing the forces and torques involved in a leg extension machine, specifically focusing on the workarm and the effects of a weight stack. Participants are exploring the mechanical structure and the forces exerted during operation, including the torque generated by the cam and the reaction forces on the shaft.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks guidance on calculating the total force exerted on the system, expressing uncertainty about whether to analyze the system as a whole or in parts.
  • Another participant questions whether the analysis is focused on the forces exerted by the user's leg or the reaction forces on the shaft, indicating a distinction between biological and mechanical analysis.
  • A later reply confirms the focus on the mechanical machine structure, clarifying the intent of the analysis.
  • One participant presents calculations for the torque on the cam and the forces on various components, including the cam, rotating bearing, and lever, but expresses uncertainty about the forces acting on the final beam where the leg exerts force.
  • The participant mentions two reaction forces and the potential for an additional weight from a person using the machine, complicating the analysis.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the best approach to analyze the forces involved, and there is ongoing uncertainty regarding the calculations and assumptions made about the system.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the forces acting on the system, the dependence on specific distances and angles, and the unresolved nature of the calculations for the final beam.

JasmineRM
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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

IMG_20150724_093216564_zps63fys364.jpg
 
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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?
 
lightgrav said:
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?
The mechanical machine structure
 
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?


IMG_20150728_090711031_zpsukf0emck.jpg
 

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