6.6 Muscle-generated joint moments

Ted collected data for a Hill-type model of muscle force production. Unfortunately, his dog ate the corner of the page, and he has to calculate the missing data. Here are the methods and results for Ted's experiment:

Methods

1. Measure parameters for the muscle and tendon:
   1. Muscle – measure peak isometric stress, optimal fiber length, peak isometric force, maximum contraction velocity, and activation time constant.
   2. Tendon – measure tendon slack length and tendon strain at peak muscle isometric force.
2. Set the joint angle to 45° (see figure below), activate the muscle to 50% of maximum, let the muscle and tendon reach static equilibrium (i.e. wait until the muscle and tendon lengths stop changing), and measure the following quantities:
   
   1. Muscle fiber length
   2. Pennation angle
   3. Moment arm
   4. Joint moment

Results

Parameters for the muscle (step 1a):

Parameters for the tendon (step 1b):

Quantities at joint angle of 45° and activation of 50% (step 2):

Help Ted by calculating the following quantities for step 2 of his experiment:

(a) Muscle fiber force

(b) Tendon force

(c) Joint moment generated by the muscle–tendon unit

You may assume the muscle and tendon have the following linear force–length and force–strain relationships: