Improving kinematic and structural performance of Geneva mechanisms using the optimal control method

Abstract

A method is proposed to improve the performance of the conventional G eneva mechanism. R ather than driving the input crank at a uniform speed, this method uses optimal control theory to synthesize the speed of the crank. In this paper, design criteria are rst developed based upon the elimination of the impact loading at the beginning and end of the motion cycle. In addition, three approaches to program the crank speed are introduced. In the rst approach, the crank speed is designed to be optimal so as to minimize the output acceleration. In the second approach, the crank speed is determined by minimizing the input motor torque. The third approach uses the degree of wear between the crank pin and wheel slot as the index to optimize the crank speed. All design objectives are formulated as a parameterized optimization problem and solved via an ef cient numerical method. F urthermore, trade-offs among the desired characteristics are taken into account by formulating the problem as a multiobjective optimization problem. Two examples are given to illustrate the design procedure.

Discussion on several forms of kinematic performance and some suggestions for the paper by Heidari et al.: An improved Geneva mechanism for optimal kinematic performance, published in Journal of Mechanical Engineering Science, 226(6), 1517–1525, 2012

“…2 The maximum normalized angular acceleration for the latter is about two times of that for the former. However, the comparison should be unfair and inconsistent.…”

Design and Experiment of Symmetrical Shape Deployable Arc Profiling Mechanism Based on Composite Multi-Cam Structure

“…A schematic diagram of the deploying process is shown in Figure 10. (16) The pitch curve of motion positioning groove and the final grooves of stationary cam are shown in Figure 9. All the grooves on lower half of stationary cam are symmetrical with upper half along X1-axis on O1-X1Y1 plane.…”

“…Giorgio Figliolini [15] proposed a composite cam mechanism with curved grooves. Jyh-Jone Lee [16][17][18] eliminated the impact load at the beginning and the end of the motion. Ion Simionescu [19][20][21] designed the self-centering statically determinate grippers, has two and three fingers, used to handle the work piece with a cylindrical shape.…”

An improved Geneva mechanism for optimal kinematic performance

“…This is a constrained single-objective minimization problem. Although the attempt by some researchers to augment the problem with more objectives including driving torque and degree of wear [14] may seem more ambitious, it could be argued that the inclusion of continuity-preserving and jerk-avoiding constraints with the single, yet the crucial objective of minimizing the wheel's maximum acceleration is far more justifiable from a practical point of view.…”

“…This method has been applied to many highperformance mechanisms to achieve modification of kinematic and dynamic characteristics [12,13]. Lee and Cho [14] used an optimal control method to improve the kinematic characteristics of the Geneva wheel. Instead of driving the input member at a constant speed, they used an optimal control method to find an appropriate variable velocity to modify some of the output characteristics, but this method needs a servo-motor or an extra mechanism to generate the required variable input speed.…”