Five points of accuracy synthesis of motion generator linkages using Maple-V

Abstract

In this paper a graphical-computational based method for design of the motion generator mechanisms with five points of accuracy using the symbolic mathematical software namely Maple-V is presented. In the first part, the problem of motion generator mechanism is defined with definition of five successive postures of a specified member. The designed mechanism must be able to locate the member in the five predefined positions. Ten poles and 10 image poles of the five successive positions of the moving plane are found in the next step. In the second part, to obtain the Burmester points of the motion, two groups of successive postures include four different set of postures are considered and for each of them one circular cubic polynomial with unknown coefficients is defined as a locus of circle points. The nine unknown coefficients are obtained using nine circle points. After determining of the equations of the two circle point curves in an implicit form, the intersecting points of the curves are found and four Burmester points are picked up from the nine possible solutions, then using the pole triangle properties, the associated center points are obtained and five successive positions of the Burmester points are obtained. All of the above procedures are done by a few commands of Maple-V. It is seen that using the prepared program, lose of accuracy arises in the graphical methods eliminated and high accurate solutions depend on the designer’s decision can be obtained. In the final part, to illustrate the abilities of the method a seven-bar linkage is designed to control effective cord length of a multiple-slat wing for an airplane.