To illustrate the application of the muscle models, we consider threetypical muscles of the arm and torso:
1. The biceps brachii, the familiar muscle on the upper arm thatflexes and supinates the forearm;
2. The pectoralis major, a large, fan-shaped muscle on the upperfront part of the chest; and
3. The brachioradialis, a muscle that twists around the elbowjoint and assists in flexing the forearm.
Two instances of the fusiform muscle model are used to representthe biceps brachii. We define two functions forspecifying the muscle’s attachments and one for instantiating themuscle. Notice that the biceps brachii is a multi-joint muscle. Itoriginates from the scapula, spans over the shoulder, elbow, and radioulnarjoints, and inserts into the radius bone. Therefore, whenspecifying the attachments of the muscle in the hierarchy, the originfunction must be called just after creating the scapula, and theinsertion function must be called just after creating the radius. Thisensures that the origin and insertion points will be transformed togetherwith their underlying parts; the scapula in case of the origin,and the radius in case of the insertion. Another action performedby the biceps brachii is supination of the forearm, an action thatis most powerful when the elbow joint is flexed to 90. In this position,if the forearm is pronated and supinated in alternation, thebiceps brachii can be seen to elongate and shorten correspondingly.Even though this motion is less dramatic in its effect on the bicepsbrachii, it nevertheless is important to simulate. The pectoralis major originates from the clavicle and the sternum and inserts into the humerus. Because of this naturaldivision into two sections, we use two instances of the multi-bellyclass to represent the muscle. The figure shows the behavior of thepectoralis major when the arm is abducted at the shoulder joint. Themodel represents the general shape of the muscle quite well, and iteven creates the armpit where the muscle bellies overlap near theinsertion into the humerus.We use the general muscle model and a simple tendonmodel to represent the fleshy and tendinous portions of thebrachioradialis, respectively. This behavior is made possible by allowingthe two points defining the mid-section of the muscle to approach each other. Recall that these points are thesecond and third control points of the cubic curve defining the muscle’saxis. As the angle between the origin and insertion section ofthe axis becomes more acute, the second and third control pointsmove closer together and the bend in the muscle’s mid-section becomesmore pronounced. Of course, if the fold is not desired, thepositions of the second and third control points can be adjusted asneeded.
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