Kinematic Singularities of Mechanisms Revisited

Abstract

The paper revisits the definition and the identification of the singularities of kinematic chains and mechanisms. The degeneracy of the kinematics of an articulated system of rigid bodies cannot always be identified with the singularities of the configuration space. Local analysis can help identify kinematic chain singularities and better understand the way the motion characteristics change at such configurations. An example is shown that exhibits a kinematic singularity although its configuration space is a smooth manifold.

Higher-order constraints for higher kinematic pairs and their application to mobility and shakiness analysis of mechanisms

“…For completeness it should be mentioned that (in contrast to the common belief) even in regular points q of V the dimension dim K 1 q may not be locally constant (i.e. q is a constraint singularity [19]). That is, the number of independent constraints may drop at q even if V is locally a smooth manifold at q (see the Goldberg 6R example in [17]).…”

“…It is common practice to assign the variables q ¼ 0 to the configuration to be analyzed. Then, C l 00 ¼ A l 00 and C k 0 ¼ A k 0 in (2) and (17), and the instantaneous joint screw coordinates in (15), (16), and (19) are simply the joint screw coordinates in the reference configuration, i.e. S i 0 ¼ Y i 0 , respectively in (31).…”