Type Synthesis of Single Loop Overconstrained 6R Spatial Mechanisms for Circular Translation

Abstract

To discover singledegreeoffreedom (DOF) singleloop overconstrained mechanisms is still an open problem. This paper deals with the type synthesis of single DOF singleloop overconstrained 6RMCTs (6R spatial mechanisms for circular translation). These mechanisms provide alternatives to planar parallelograms and are also associated with selfmotion of several translational parallel mechanisms. 6RMCTs are to be obtained using a construction approach in combination with the approaches to the type synthesis of parallel mechanisms. By imposing certain conditions on the hybrid overconstrained 6R (planospherical, planoBennett, doublespherical, and sphericoBennett) mechanisms, Bricard plane symmetric mechanism, and Bricard line symmetric mechanism, six special cases of 6RMCTs are obtained. By combining planar parallelograms with these special mechanisms, the general cases of 6RMCTs are then constructed. Finally, 4R2H, 2R4H, and 6H mechanisms for circular translation are obtained from the above 6RMCTs by replacing one or more pairs of R (revolute) joints with parallel axes each with a pair of H (helical) joints with parallel axes and the same pitch. This work contributes to the research on overconstrained sixbar mechanisms and further reveals that the research areas of parallel mechanisms and singleloop overconstrained mechanisms are closely related.