This proposal should be taken with a grain of salt (hell, the whole shaker) since it was written before I had looked into the problem that deeply. Still, it makes a very reasonable overview.
Short Form Proposal (circa April)
An attempt will be made to model the kinematics of prehensile tails (such as those of monkeys) with an eye towards possible construction. The basic road map would be to begin from the wave equation in three dimensions, with one end free and the other end fixed and the source of forcing functions. Possible second order approximations include modelling the tail as a series of links with three degree of freedom connections, an arbitrary number of which are able to fix their relative position, or as a flexible cylinder arbitrary sections of which can be put into tension (i.e. tendons). Other ideas can likely be found through an examination of snake-like manipulator arms.
I realize that the topic of this projects might require some justification. The best I can do is to state that I love the way that animals move, that there is something otherworldly about it, and a large part of that is their different body shapes. The capture some part of that, especially the dynamics as well as the aesthetics, would be wonderful. If I ever learn how to do things in the machine shop, I would love to build this. Then next year, I will make cat's ears.