Existence Criteria for Over-Constrained Mechanisms: An Extension of Motor Algebra

The new concept of a mobile screw space is introduced in this paper. A mobile screw space is a set of motors for which the outer product of any two arbitrary elements belongs to the original set. It is shown that the condition for the existence of almost all existing over-constrained mechanisms is related to the mobile screw space, that is, all joint motors of the mechanism either belongs to a mobile screw space or belong to a space which is given as the sum of mobile spaces. Determining an over-constrained mechanism on the basis of this condition makes it possible to generate many mechanisms, including most presently known over-constrained mechanisms.