Detection of Isomorphism of Kinematic Chains Using two DOF Using CSJV Matrix

Identification of isomorphism among the kinematic chains and their derived mechanisms have broad area of research work for previous some decades. An advance approach for generalization of kinematic chains uses identical links but disparate kinematic joint. in present work, utilizing the link–link type of transformed matrix (TM) and components of matrix has been selected as one and zero depending on the presence or absence of a relation in between the revolute joints. We detected the kinematic chains applying same link and sliding pair and all turning pairs and identify the isomorphism, but must be distinct. To reduce this problem, we try to improve disparate set of matrices called Sum of Cube of Joint Value Matrix (SCJVM), that is joint–joint types of matrices are used. In this paper, an approach based on Bocher’s formula is presented to identify all isomorphism and distinct mechanisms with different links and tests for two degrees of freedom. The suggested method was examined based on various problems from 5 & 7-links and two degrees of freedom. All solutions have been ascertained satisfactory results with prevailing literature. The CSJV matrix is capable to differentiate the type of kinematic pairs (pin joints) between two links. These characteristic or peculiarity polynomials are also capable to identify isomorphism having simple jointed kinematic chains, multiple or poly jointed kinematic chains and furthermore kinematic chains with co-spectral graphs. The expression of peculiarity polynomial expression can potentially convey certain characteristics and properties of mechanisms. Utilizations of five-bar kinematic chains like robotics linkages find applications across a wide spectrum of areas, spanning from prosthetic limbs to tactile response systems. This design has been examined in various tactile feedback devices to provide overall force sensations. Seven-bar linkages possess two degrees of freedom, making it suitable for various machines that require variable paths of motion. © 2024, The Institution of Engineers (India).