Abstract: Based on screw theory, the relationship among the numbers of constraints, joints and degrees of freedom that constitute single closed-loop over-constraint mechanism are analyzed. Also the calculation formula of the degree of freedom for single closed-loop over-constrained mechanism is presented. Moreover, over-constraints are classified into two types of forces and couples which have different orders, in terms of reciprocal screws. All possible forms of characters of independent over-constraints and numbers as well as their combinations are summarized. Under the condition of having a given special combination over-constraints, by using the principle of virtual work and taking reciprocal screw theory as calculation means, the structural synthesis method for the multi-degree of freedom single closed-loop mechanism is obtained. The non-instantaneous conditions of mechanism are obtained by using analytical method, and axis layout, number, arrangement and spacegeometric conditions of joints are presented. The problem for synthesis of multi-DOF single loop over-constraint mechanisms is solved systematically and wholly and all the possible single closed-loop over-constrained parallel mechanisms are enumerated. The structure synthesis procedure, and design examples of some typical mechanisms are given.

Key words: Degree of freedom, Over-constraint, Screw theory, Single closed-loop mechanisms, Synthesis