Gradient method for identification of isomorphism of planar kinematic chains

AbstractDetection of isomorphism among large family of kinematic chains is always a challenge and numerous methods are also proposed with their inherent strength and weaknesses. Gradient concept is presented for identification of isomorphism and inversions of kinematic chains. In the present work, based on gradient analogy, gradient matrices are proposed to distinctly denote the structure of each kinematic chain. Further, First gradient chain string and Second gradient chain string two invariants from the matrix in the form of strings are identified to be used for detection of isomorphism and similarly First gradient link string and Second gradient link string and First gradient chain string of inversion are formed for detection of inversions. The proposed novel method is easy, exhaustive and reliable. It is applied successfully for detection of isomorphism and distinct inversions to all known families of kinematic chains i.e. single degree of freedom, multi degree of freedom, and detection of isomorphism...