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.