A Systematic Formulation of Overconstraint Conditions in Kinematic Chains by Displacement Groups

The paper describes a systematic approach to define geometrical and dimensional overconstraint conditions for single-loop kinematic chains of both “banal” and “exceptional” type. The approach is an application of the theory of displacement groups . It presents several interesting features: it can be easily integrated with mobility analysis; it makes use of geometric data local to links and does not require a preliminary mechanism assembly nor a given initial congruent position; it is systematic and can be suitably implemented in a computer code; it suggests where geometrical and dimensional tolerances have to be located; it can be embedded in other group-based approaches, like kinematics synthesis or dynamics analysis. After a brief summary of the properties of displacement groups and their operations, the paper shows how they can be used to formulate systematically the overconstraint conditions in kinematic chains. A computer implementation of the approach is also outlined, and several examples with different complexities are given.