Calculation of the General Number of Imposed Constraints of Kinematic Chains

The study provides derivation and application of novel formula for the calculation of general imposed constraints for kinematic chains (including mechanisms and zero-degrees-of-freedom Assur groups) depending on the types of kinematic pairs and numbers of movable links. The presented formula is adopted for all mechanisms families and may be used for kinematic chains with various DoF. The study proves existence of kinematic chains which include parts from different families having diverse numbers of imposed constraints. Provided formula allows not only to calculate number of constraints, but it can be also used for the task of structural synthesis of kinematic chains, for identification of mobility of a whole system, numbers of movable links and kinematic pairs as well as their types depending on the technological requirements.