Bricard one-DoF motion and its mechanical generation

• Bricard one-DoF motion (BM) is a spatial motion with all spherical trajectories.
• Invariance characteristics and a visualization of three types of BM are provided.
• Isoconstrained, exceptional, or paradoxical mechanical generators are proposed.
• The platforms having BM are clearly explained.
• General GD platform and Verheyen-type mechanism with or without offset are revealed.

Bricard one-DoF motion (abbreviated to BM) is a type of spatial motion in which all points of the moving body have spherical trajectories in the three-dimensional (3D) Euclidean space. This paper focuses on the mechanical realization of BM. The invariance characteristics and a visualization of three types of BM are provided in detail and the criterion for a possible full revolution is clarified too. The primitive Bricard motion generators (BMGs) are first proposed and geometrically verified. With the synthetic reasoning via the self-conjugation of any cylindrical 1-DoF motion and the invariance property of BM, two or more-loop BMGs are then synthesized systematically. These BMGs include isoconstrained mechanisms and overconstrained ones and the latter are exceptional and paradoxical chains. Besides, the platforms having BM, such as the Wren platform, LADD motion converter, algebraic screw joint, Griffis–Duffy (GD) type platform, etc. are clearly explained. A generalization of the GD platform and the general Verheyen-type mechanism with or without offset are newly revealed as well.