On the solution of region-based planar four-bar motion generation

Burmester curve-based motion generation can produce an infinite number of solutions for given four rigid-body poses. It is difficult for designers to synthesize the best linkage through rapidly and precisely selecting curve points that ensure to satisfy every design condition. To solve this problem, in this paper, different circle point curve equations are unified into the same form with the angle φ (φ ∈ (0, 2π)) as the parameter firstly, thus, an infinite number of rigid-body guidance solutions can be expressed on the finite solution regions through setting up the reflection relationship. Based on initial analysis of solution regions, the mechanism property graph has been computed to make the designers find out involved mechanism information, such as their types, minimum transmission angles, link-length ratios, defects, and so on. Secondly, after design constraints are considered and imposed, feasible solution regions which avoid aimlessness in choosing positions can be calculated. Finally, on the feasible solution regions or the one of interest, property analysis graphs are displayed, along with which the optimized rigid-body guidance solution can be produced. The method in this work is simple, highly accessible and convenient for application in practice.