Enumeration of basic kinetic chains with simple and multiple joints

Generating functions for mechanism specialization

“…If the joint set (J) of the (8,9) kinematic chain kinematic chain shown in Fig. 13(a), whose permutations are given in Fig.…”

“…In this latter, each kinematic chain is specialized through the assignation of link and joint types to obtain all possible mechanism configurations. Type synthesis and mechanism specialization have been the subject of many studies , which have variously based the structural synthesis of the kinematic chains on the graph theory [2][3][4][5][6][7][8][9], a characteristic polynomial [10][11][12][13][14][15][16], or approaches based on codes [17][18][19][20][21][22][23][24][25], matrices [26][27][28], or other elements [29][30][31][32][33][34][35][36][37][38][39]. In some such investigations, a generation of the multiple kinematic chains or mechanisms during the synthesis and specialization processes requires complex procedures for the detection (or computer-aided assignation) and deletion of isomorphic mechanisms [40][41][42].…”

“…25 shows 16(8,10) kinematic chains with one degree of freedom, each of whose permutations are given inFig. 26.…”

“…The inversion o1 of an (8,10)-o kinematic chain is fixed to link A, with which joints a, b, e, and h are incident, meaning that they are not exchangeable with other joints and the permutations remain p 1 to p 6 . The mechanism's joint set (J) can be partitioned into four subsets, J 1 (a), J 2 (beh), J 3 (cfi), and J 4 (dgj).…”

Algorithm for computing the connectivity in planar kinematic chains and its application

“…1,2 During the last several decades, numerous methods have been developed to synthesize various kinds of kinematic chains, including simplejointed [3][4][5][6][7][8][9] and multiple-jointed chains. [10][11][12][13][14][15] The number of synthesized kinematic chains is usually so large that it is hard or impossible to evaluate individual characteristics of each chain. Therefore, in practical application, some parameters are used to classify the kinematic chains, and restrict the number of chains required to be considered.…”