Session: 06-01-01 Product And Process Design

Paper Number: 94271

94271 - Reversible Geometric Constraint Programming on Kinematic Analysis and Synthesis of Planar Linkages 

This paper proposes a novel approach to do the kinematic analysis and synthesis for higher-order motion by using commercial computer-aided design (CAD) software. To synthesize a linkage, this paper takes advantage of the geometric constraint, the aid of similar triangles, and the concept of the traditional velocity and acceleration polygons. The step-by-step method of reversible geometric constraint programming is proposed. The major contribution of this paper is to synthesize the linkages with the prescribed velocity and acceleration of either the output link or the coupler link, which is traditionally difficult. In the past, to design a linkage with precise higher-order requirements of a coupler point, one needs to learn the Euler-Savary equation or the order synthesis of Burmester’s theory, which are computationally hard and require advanced kinematic knowledge. On the other hand, since the analysis procedure is much simpler, an alternative method is to adjust the dimension of the linkage until the analysis data are approximately close to the requirements. However, the method may be time-consuming and does not guarantee the results. Hence, the proposed approach requires less knowledge and gives the closed-form solution that fulfills the higher-order demand. Based on the graphical interface, the proposed approach is intuitive and easy to operate and shows the physical meaning of the linkages. Since the velocity and acceleration polygon are plotted on the sketch, the approach shows the analysis results at the time when the synthesis process is finished. This reduces the analysis process of making sure the synthesis results are correct, in the traditional analytical approach. This paper demonstrates the procedure by three examples. The first example synthesizes a four-bar linkage with a prescribed velocity ratio. Secondly, a four-bar linkage with its coupler curve has a second-order straight line segment is synthesized by assigning the same direction of the velocity and the acceleration of the coupler point. Thirdly, a single dwell Stephenson six-bar linkage is synthesized. The third example shows the generality of the approach and the ability to deal with prismatic joints and more complicated linkages. The proposed approach can be used as an ideal tool to teach undergraduate students about kinematic analysis and order synthesis. Since the approach is based on the graphical approach concept and computer drawing, it is simpler to understand, memorize and implement. The approach proposed by this paper completes the synthesis theory of geometric constraint programming for planar linkages and it may have the potential to make analysis and synthesis of spatial linkage easier.

Presenting Author: Cody Leeheng Chan National Taipei University of Technology

Presenting Author Biography: Cody Leeheng Chan got his Ph.D. in Tennessee Tech in 2021. He is a research assistant professor in Taipei Tech, Taiwan. His research interest includes theoretical kinematics, gear profile design, and computer-aided linkage synthesis.

Authors:

Kwun-Lon Ting Tennessee Technological University
Cody Leeheng Chan National Taipei University of Technology