Type synthesis of variable-DOF single-loop spatial mechanisms using Bennett 4R mechanisms and Goldberg 5R mechanisms

This paper deals with the type synthesis of variable-DOF (degree-of-freedom) single-loop spatial mechanisms — a class of reconfigurable mechanisms that DOF may change. A construction method is proposed to the type synthesis of variable-DOF single-loop mechanisms using Bennett 4R mechanisms and Goldberg 5R mechanisms. Using this approach, variable-DOF single-loop mechanisms can be obtained by first constructing multi-DOF multi-loop overconstrained mechanisms and then obtaining multi-DOF single-loop overconstrained mechanisms from these multi-DOF multi-loop mechanisms. Six types of variable-DOF single-loop 7R mechanisms and three types of variable-DOF single-loop 8R mechanisms have been obtained. No variable-DOF single-loop n R (n8) mechanisms can be constructed using Bennett 4R mechanisms and Goldberg 5R mechanisms. Isomeric variations of these variable-DOF mechanisms can be further obtained by isomerization. This work provides a solid foundation for further investigation on variable-DOF single-loop mechanisms.