The 12-muscle, 4 degree-of-freedom robotic arm idea
The idea was to activate the arm of a medical-supply human skeleton replica, using servos to mimic muscle contraction, in series with elastic tubing to represent the elastic nature of muscle-tendon combinations. The shoulder was to have three degrees of freedom described with a 3-1-3 Euler angle sequence. The fourth degree of freedom was a simple hinge joint at the elbow. The idea proved a bit over-ambitious for a first attempt at a robotic arm, but it will return, better than before! I completed an in-depth development of the equations of motion for this arm, with muscles excluded, and the results will be posted on a page here when I get around to it. The results were intriguing, and some of the related graphics turned out to be quite stunningly beautiful (see bottom of this page). Check back in a while for more if you are interested.?>
This is a table of the muscles that were to be included on the arm. The proposed muscles depicted with elastic tubing.
Each muscle was to be modeled using a servo, some strong fishing line, and an elastic tubing element, as shown below. This idea was realized in our two-degree-of-freedom arm with its six muscles (see the appropriate page when it is completed).
Muscle-tendon units are modeled using a hobby sail-winch servo,
strong fishing line, and a section of elastic tubing.
The mathematics of the 4DOF arm was quite complicated, but fascinating. Below are two 3D projections of some of the surfaces of singularity that appeared in the original equations of motion for the 4DOF arm. Trajectories through state spaceare shown in green. I will include the equations here when I get around to it.