Bench press machine

Introduction

In the past fifty years, different location dedicated to fitness have made their apparition all over the world. With them, many training types. One of these style of training uses machines that constrain the movement, isolate the working muscle and reduces the risk of injury. Those machines are controversial in the community and are said to mislead the user.

The controversy is linked with the long time used of those machines and the absence of development in stabilizing fiber muscles. The stabilisers are essential in real world application and this weakness will cause injury. In this paper we will focus on the misleading part witch concerns more the engineering sector.

To evaluate how exactly the industry is convincing users that they are stronger than they really are we will analyse the dual grip press machines. This machine is marketed as a trainer for the pectoral muscles. Each arm is independent from the other to prevent a stronger side to compensate for the other. The picture on the left represent a typical machine of the type studied while the picture on the right is a representation of the pectoral muscles.

BenchMachinePectoralImage

The machine misleads the user in two ways. The first one is linked with the used muscles. It is believed that shoulders play a bigger part than advertised. The user trying to isolate is pectorals will not get what he wants. Secondly, the combination of the lever arm effect and the pulley system will reduce the actual strength needed to lift the weight.

Objectives

The objective of the analysis will be to first confirm that the machine is misleading and if true to quantify the proportions.

The fist step will be to evaluate the equivalent weight the user is pushing on the handles. The second step will be to divide this force in its X and Y component. The X component of the force would come from the pectorals and the Y component comes from the shoulders. Every force is transformed in weight to give a reference basis.

The modelling problem

To model this problem various steps are needed. The 3D modeling will be done in Solidworks to save time as the software is built especially for this purpose. The integration of joints, motion and the pulley system will be done in Adams View.

Solidworks:

Structure

The first part of the 3D modeling is to generate the general structure. The bench is already added and will be in the same materials (steel) as the other parts. It will not have an impact on the result of the analysis and is present as a visual aid.

Structure with accessories

The weight blocks and arms are subsequently added. So far there is no link between them so only their placement and geometrical proportions are considered.

Pulley

A pulley model and its support are created on a different file. This step will be remade trough Adams cable system, but it will be facilitated a lot as the placement will already be determined.

Structure with pulleyPulley triangle

 

The last part of the 3D modeling was to do an assembly with the pulleys. A lot of thought went into this process to respect the possible direction change of the so far hypothetic cable. To allow the independent movement of the arms the cable system is divided in two. The upper part will loop trough the two higher pulley (picture on the right) and the lower system will pull on the bottom one. This section will be made clearer with videos of the moving part.

Adams:

To transfer the Solidworks model to Adams it must be converted in a .STEP file. Then a series of constraint and features where added to reproduce the working condition. The first list is a summary of them while the next two pictures are an exhaustive list.

  1. Fixing all the pulleys to the frame except the pulley triangle which is fixed to one another.
  2. Fixing the frame to the ground
  3. Revolute joint in the arms axis or rotation.
  4. Fixing the cable anchor to the arm as they where imported as two different part with the .STEP file.
  5. Translational joint in the weight and the pulley triangle to prevent lateral movement.


Cattura2Cattura

Two motions where added as rotational displacement in the arms to simulate the movement made by the user.

Three contact where added as impacts. Between each arm and the frame to have a proper equilibrium position. The third one is between the weight and the frame.

Finally, the cable and pulley system were placed. To do so a general pulley property was inputted so it would be the same dimensions as the system created in Solidworks.

General Pulley properties

 

The 16 pulleys where placed using the placement from the .STEP file. After this step all the original pulleys where deactivated having served their purpose.

Cable properties

The cable is then added with proper enrolment around the pulleys. The only changes made in the cable parameters where linked with the Young’s Modulus and the solver which was activated. The Young’s modulus was significantly increased to prevent the cable from stretching during the movements.

To properly simulate the system every object was defined as steel a commonly used metal in the industry for its price, durability and relative ease of wielding.

Solver properties:

Initially the system was failing to produce proper movement. Mistakes such as the arms leaving their axis of rotation and the contacts jumping where common. Simulation failure was also a recurring sight. To solve the problem a combination of WSTIFF and SI2 where used. It lengthens the solving time but provides a more stable simulation.

Movement videos from two point of view. The first one shows the general system in action while the second one shows the pulley triangle moving:

Simulations and analysis of results

First question was to evaluate how much strength came from the shoulder compared to the pectoral muscles. To calculate the total force the torque on one of the arm axis was measured and then divided by the length of the lever of arm.

Force Graph

First, we noticed that the required strength varies across the movement. This is due to the angle of the cable witch changes with the rotation. By care of transparency it must be mentioned that between 0 and 0.098 second, improbable results appear. In this time laps the strength goes from thousands of newtons to the expected results. This might be caused by the contacts behaving in an unexpected way. Those values where excluded from the analysis as they represent no physical known force in this system.

From the resulting force in the handle, its X and Y component where extracted to solve the initial question. The X axis being the pectoral strength and Y axis being the strength from the shoulders. Both where then divided by the gravitational acceleration to obtain an equivalent mass.

Formula Kilograms per muscle graph

This graph confirms long held suspicions regarding the machine required muscles. It does use mainly the pectoral muscle, but its use of the shoulder gets bigger as the movement progresses. It is worth mentioning that the sum of each muscles is not equal to the total mass. The systems resultant forces are dependant on Pythagoras theorem. Considering that more power is required from other muscles we could stipulate that a higher caloric burn rate is in effect than a real isolation exercise.

The second question is to evaluate the difference between the selected mass the mass the users will push. To do so we ran the simulation sixteen times whilst changing the mass of the weight by ten kilograms each time. Using the last graph presented we compared the total mass at 2.28 second (about 28 degrees). We multiply that mass by two since two arms are pushing. We finally divided the total mass in two arms by the selected weight to obtain a ratio between the two.

Table of selected to pushed weight

These results are also presented in the next two graphs.

Progression Graph

In this graph we can see that there is a linear progression between the selected weight and the users required strength. It means that the athlete will be able to keep a constant progress without worrying about how the machines design will affect him. At least in this specific movement.

Ratio Graph

Finally, in this sport people have a strong tendency to compare to each other by the weights they are lifting. This graph proves that they should never compare work done on the machines with work done using free weights. There is also a logarithmic tendency so that the bigger the weights the less it is possible to compare them to each other.

Conclusion

The goal of this analysis was to model a dual grip bench press machine to evaluate its movement. To do so, the machine geometry was modeled in Solidworks. Then the movement constraint and the motions where added. It was then possible to measure forces in certain points. From these measures we where able to calculate the component of these forces to answer our question.

Through the analysis we determined the proportion of shoulder to pectoral used in the movement. We where also able compare the lifted charge to their equivalent in free weights. It was successful in demonstrating the machine is indeed misleading the athletes in its use.

In a subsequent study it would be quite interesting to model a simplified version of the human body and have the motion come from the ligaments. The pectoral muscle per example pulls on three different ligaments to achieve its movement. We also neglected the use of the triceps which would have reduces the loads in the pectoral muscles.

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