The angular capacity of spherical joints used in mechanisms with closed loops and multiple degrees of freedom

Typical kinematic and dynamic analysis of mechanisms considers the joints just as theoretical constraints. Nevertheless, for some particular kinematic joints (e.g. spherical joints) the physical realization takes the shape of distinct components that are attached to the adjacent bodies. While a spherical joint allows three theoretic relative rotations, except the self rotation of the shaft the other two rotations have a reduced range because of constructive limitations. In this paper we propose a function named angular capacity to represent the range of the physically permitted motion in a spherical joint. A graphical representation of the angular capacity is also proposed to intuitively illustrate the relative motion range and the constructive parameters that influence it are identified. Angular capacity of a spherical joint is defined as a constructive feature of the joint assembly—out of the mechanism context—but also as a motion range demanded by the mechanism from the spherical joint. For the first case general relations have been proposed for the constructive angular capacity calculation and useful consideration has been made for the embodiment design of the spherical joints. For the latter, a complete methodology and relationships for mechanisms with two degrees of mobility are proposed as well. Finally, the suspension-steering mechanism of the passenger cars is presented as a use case.

► A representation of the relative motion has been proposed, named “angular capacity”.
► A methodology for analysis of constructive angular capacity has been proposed.
► A methodology for the angular capacity in a spatial mechanism has been developed.
► Angular capacity is illustrated for the suspension mechanism of passenger cars.