(1.a/b)
1.0 Objective:
To design a computer model of the upper and lower arm during a 'bench-press' maneuver which estimates muscle forces. To appreciate the effects of different muscle insertion points on these estimated muscle forces.
2.0 Background:
Based on the model you developed for the first computer project you are to expand on it by adding two pair of muscles which act at the shoulder and elbow. The basis for you model is described below.
As mentioned in laboratory 2, one way to simplify
the static equilibrium equations (2.a/b/c in laboratory 2) is to assume
the muscles act along a line such that muscle force can be calculated by:
(1.a/b)
Where lf and le are the flexor and extensor lines of action.
There are many different ways to calculate a given muscle's lines of action. For this computer project, you will use a method based on the seemingly overly complicated figure 1.
Figure 1: Model of arms and muscles during the bench press maneuver.
We begin our analysis of figure 1 by first noting that in our first computer project we already defined points S (shoulder), E (elbow) and W (wrist). We therefore know that segment SE is the lower arm and segment EW is the upper arm. We also know that the angle between segments SE and EW is the elbow angle qEand the angle between SE and the ground is the shoulder angle qS. OK now on to the new stuff!
Consistent with the method of muscle modeling described in lab 2, we assume that both joints (shoulder and elbow) have only 1 pair of muscles (flexor and extensor). These muscles are represented by the gray dashed lines on figure 1. We'll also assume that each muscle has an origin and insertion point (labeled as points IE/S and OE/S in figure 1). Finally, we'll assume that these musclular lines of action also pass through an 'action' point (labeled A) adjacent to the joint. Thus point AEf represents the action point for the flexor muscle about the elbow, AEe the action pont for the extensor about the elbow and the same notation would follow for the shoulder.
Using this method for calculating each muscle's line
of action we can calculate the direction of muscular force. For example,
looking at the elbow we have the flexor's line of action defined as:
(2) 
Let's see how all of this can be applied to our simple model. First we take the segment EW in isolation and draw the free body diagram as seen in figure 2.
Figure 2: Free body diagram of segment EW.
Applying the condition of static equilibrium to the free body diagram seen in figure 2 we have:
(3.a/b/c) 
Notice in equations 3.a/b/c there are a total of 4 unknowns and only 3 equations. This is the same problem as we had in laboratory 2, namely we don't know the level of flexor/extensor co-contraction. You must decide on a method for determining the ratio of flexor/extensor co-contraction to estimate muscle forces, unfortunately as you will see while searching the literature, there is no currently widely accepted way of calculating this ratio. Your task will be to choose some criteria from the literature for determining the level of co-contraction and implement it in your model.
3.0 Model Data:
The parameters to be used in your model are as follows:
To investigate the effects of varying insertion points of the muscle, have a total of 3 different insertion lengths (75%, 100%, 125% of the original length) for both the shoulder and elbow.
4.0 Report and Model Requirements:
Again you can use any software package that you wish to perform the calculations (MATLAB is highly recommended). The report (less than 10 pages) is due at the end of the term (12/06/99) and should include the following: