Abstract
Equilibrium rotations of a planar kinematic chain undergoing a single degree of freedom (out of plane) rotation in a gravitational field are studied. Sharp bounds on the number of dynamic equilibria are given, and the dependence of this number on physical parameters is discussed for the special case of two-link chains and chains with identical links. The theory indicates that there will be a richer set of dynamically stable equilibria for carefully designed chains with unequal links. This is born out by laboratory experiments.

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