Three Novel Symmetric Waldron–Bricard Metamorphic and Reconfigurable Mechanisms and Their Isomerization

This paper explores a class of metamorphic and reconfigurable linkages belonging to both Waldron's double-Bennett hybrid linkage and Bricard linkages, which include three novel symmetric Waldron–Bricard metamorphic and reconfigurable mechanisms, and further presents their three extended isomeric metamorphic linkages. The three novel Waldron–Bricard metamorphic and reconfigurable linkages are distinguished by line-symmetric, plane-symmetric, and line-plane-symmetric characteristics. The novel line-symmetric Waldron–Bricard metamorphic linkage with one Waldron motion branch and two general and three special line-symmetric Bricard motion branches is obtained by integrating two identical general Bennett loops. The novel plane-symmetric Waldron–Bricard reconfigurable linkage with two plane-symmetric motion branches is obtained by coalescing two equilateral Bennett loops. The novel line-plane-symmetric Waldron–Bricard metamorphic linkage with six motion branches is obtained by blending two identical equilateral Bennett loops, including the plane-symmetric Waldron motion branch, the line-plane-symmetric Bricard motion branch, the spherical 4R motion branch, and three special line-symmetric Bricard motion branches. With the isomerization that changes a mechanism structure but keeps all links and joints, each of the three novel Waldron–Bricard linkages results in an extended isomeric metamorphic linkage. This further evolves into the study of the three isomeric mechanisms. The study of these three novel metamorphic and reconfigurable mechanisms and their isomerization are carried out to demonstrate the characteristics of bifurcation and to reveal motion-branch transformation. Furthermore, by exploring the intersection of given motion branches and using the method of isomerization, more metamorphic and reconfigurable linkages can be discovered to usefully deal with transitions among possible submotions.