Partitioning instantaneous degrees-of-freedom and its application to three-degrees-of-freedom parallel manipulators

摘要

In general, a rigid body moving in space can possess three translational and three rotational degrees-of-freedom. In many situations, the motion of the rigid body is constrained, and therefore has less than six-degrees-of-freedom. In such cases, it is often important to understand how the degrees-of-freedom are distributed between pure translation and pure rotation. In this paper, we present a general approach towards the partitioning of the available instantaneous degrees-of-freedom for the constrained motion of rigid-bodies. The approach is based on computing the eigenvalues and eigenvectors of certain matrices associated with the instantaneous motion of a rigid body. The eigenvalue problem involves the solution of at most a cubic polynomial, and hence the eigenvalues can be obtained in closed form in all the cases. The approach is applied to several well known three-degrees-of-freedom spatial parallel manipulators. It is well-known that parallel manipulator can gain one or more degrees-of-freedom at a gain-type singularity. The general approach is also applied to determine if the gained degree(s)-of-freedom are in translational or rotational in nature.