Directed structural synthesis of optimal planar mechanical systems with complex pinjoints (mechanisms, pin frameworks, Assur groups, robots). Part 1

The paper presents the structural formulas and the four basic mathematical theorems of a single structural model which provides a basis for all having been found integral solutions to compose the universal structural tables containing a complete list of standard calculation codes for optimal structures with the use of both simple and combined joints with different degrees. Based on the standard codes from these tables the direted structural synthesis of one, two and three degreesoffreedom mechanisms, rod trusses, special Assur groups, one and many armed robots and manipulators has been performed. The atlas of four sixmembered nonisomorphic kinematic chains has been composed and the existence of 14 structural diagrams of 6membered one degreeoffreedom linkages with combined double hinge has been found.