Number structural synthesis and enumeration process of all possible sets of multiple joints for 1-DOF up to 5-loop 12-link mechanisms on base of new mobility equation

•The enumeration process of all possible set of multiple joints was done algebraically.•A general method to synthesize all possible sets of multiple joints for multiloop mechanical systems is proposed.•We use a new mobility equation and basic theorems for K-loop, F-DOF multiple joint kinematic chains.•All 1-DOF non-fractionated and fractionated chains with multiple joints up to 5-loop 12-link are obtained.•The atlas database, containing sets up to six-pin multiple joints, with νmax= 8 multiple joint factor is established.

This article considers a creation of multiloop multiple-jointed kinematic chains. It presents numeral and topological decision of the mechanical tasks which determine all the possible integer sets of multiple pin-joints for a number of structural synthesis of multiloop non-fractionated and joint-fractionated kinematic chains [by the classification proposed by H. F. Ding, B. Zi, P. Hung, A. Kecskeméthy, Mech. Mach. Theory 2013 70 (12) 74–90]. This research uses Pozhbelko's unified method of directed structural synthesis and analysis based on a new mobility equation (degrees of freedom) for as well as simple-jointed and multiple-jointed multibody mechanical systems with given number of independent loops and degrees of freedom. All the 95 possible and acceptable set combinations up to 6-pin multiple joints for up to 12-link and up to 5-loop kinematic chains are obtained for the first time. Finally, the paper presents atlas database which consists of 95 technique nonisomorphic non-fractionated and fractionated kinematic compositions with indication of all the possible sets of multiple joints, representing the 4 set for six-link, 10 set for eight-link, 25 set for ten-link and 56 set for twelve-link for 1-DOF multiple joint mechanisms in batch.