On Realization of Spherical Joints In RSSR Mechanisms

A spherical joint must allow adequate mobility between the ball and socket. Unless the specific geometric requirement of the spherical joint, namely the trajectory of the ball stem in the socket, is known, the realization of a synthesized mechanism containing a spherical joint can become an endless trial and error process or even a fruitless attempt. Typical examples can be found in RSSR mechanisms. For a synthesized RSSR mechanism, this paper presents the closed form equation describing the spherical trajectory of the ball in the socket and the design and manufacturing issues of the spherical joints. It offers the classification scheme of spherical joints based on the required ball rotatability in the socket and shows how the necessary socket opening of the spherical joints is affected. The size and location of the socket in a spherical joint must be properly determined to meet the rotatability requirement and in many situations, a conventional spherical joint with a circular socket opening cannot be used. Essential geometric and location information regarding to the use of non-circular socket opening, spherical grooved pair, as well as revolute joints to replace the conventional spherical joints to realize a synthesized RSSR mechanism is presented. The proposed concept and method can be extrapolated to other mechanisms containing spherical joints.