A Study On Kinematic Synthesis Of Adjustable Mechanisms For Function Generation

Multi-axis open-loop robots are under-utilized and the cost of maintenance is relatively high, when they're used in limited similar tasks. On the other hand, conventional automation mechanisms are comparatively simpler in structure, but lack in flexibility. Even though the adjustment of the task is very little, the mechanisms have to be redesigned. In adjustable mechanisms, the dimensions and/or the positions of one or several particular links can be adjusted so that the mechanisms can generate different tasks. They have the advantages of above two while overcome their disadvantages. This paper takes adjustable linkages as research objects, and investigates kinematic synthesis of adjustable linkages for function generation and solutions to highly nonlinear synthesis equations. The outcomes obtained are as follows:Kinematic synthesis models of planar 6-link Watt-type linkage, planar 6-link slider linkage and planar 7-link 2-DOF linkages for function generation are set up. A set of nonlinear equations of precise synthesis of each linkage are established. The adjustment of pivot position of the middle link in planar 6-link Watt-type linkage is classified. The corresponding constraint equations of each mechanism are presented. The relationship between the number of the tasks, precision points, constraints and free choices of variables in each model are analyzed. The mathematical models of optimal syntheses are set up and solved for special case.A kinematic synthesis model of RSSR linkage in which the angle between input and output axes is right is set up for function generation. The relationship between the number of the tasks, precision points, constraints and free choices of variables is analyzed. A set of nonlinear equations of precise synthesis are established for special case according to co-planarity and equal distance conditions. By resultant elimination, 3 polynomial equations containing 3 variables are obtained. All of the groups of real solution within a certain value range are generated with computer graphic method.In order to solve the above 3-variable polynomial equations of high order, a program is made with the mathematical analytical software-Mathematica. A variable is sampled in a certain increment, and introduced into the equations. There are two sets of any two equations to be solved. The real solutions of the two sets are protracted in spatial coordinate system to obtain two curves, so that the intersection points of the two curves can be found as the solution of the original equations. For the special case one of original equations contains only two unknowns, these two variables can be sampled firstly, and then introduced into the other two 3-variable equations. The real solutions obtained are spread along the cylindrical contour curve, so that a two dimensional graph which is easy to observe is generated. The corresponding spatial points of intersection are found through the points of intersection of the two curves in this graph. By taking these spatial points as initial guess, all exact real solutions within a certain range of variables are found using unrestraint optimization.