Synthesis of Four-bar Motion Generation Considering Worst Case Joint Tolerances
Abstract— Four-bar motion generation is used to synthesize a mechanism which passes through or approximate prescribed rigid-body positions. This work will discuss the motion generation of four-bar mechanism with position tolerance variations due to joint running clearance. The tolerance variations study will be based on the standards of American National Standard Institute (ANSI). The new design constraint introduced in this paper will consider the joint tolerances and incorporate it into the displacement position matrix of coupler points described in the conventional planar four-bar motion generation models. The synthesized planar four-bar mechanism will produce tolerance limits for moving pivots and link length from which any mechanism can be synthesized to satisfy the prescribed coupler points with their prescribed tolerances. The included example demonstrates the synthesis of a four-bar mechanism with joint tolerances. 1
The direct linearization method applied to position error in kinematic linkages
This paper demonstrates the direct linearization method (DLM) applied to position error in kinematic linkages due to link-length and angle variations. It combines the mathematical techniques used in assembly tolerance analysis and kinematic error analysis to demonstrate a method that is applicable to models that can be described using vector loops. A bivariate model using DLM is introduced and compared to other deterministic and probabilistic methods using a multiple-loop mechanism as an example. The bivariate model is shown to be an efficient and accurate means of estimating the position error in kinematic linkages.
Optimal synthesis of crank–rocker linkages for path generation using the orientation structural error of the fixed link
Abstract This paper introduces the concept of orientation structural error of the fixed link and presents a new optimal synthesis method of crank–rocker linkages for path generation. The orientation structural error of the fixed link effectively reflects the overall difference between the desired and generated paths, avoids making point-by-point comparison between the two paths, and requires no prescription of timing. The optimal synthesis model is set up based on the orientation structural error, and the global optimal solution is obtained by a genetic algorithm. The effectiveness of the proposed method has been demonstrated on two synthesis examples.