The objective of this paper is to synthesis spherical four-bar motion and path generators using continuation method (homotopy method). Using continuation method, we may obtain a complete set of the solutions to the problems, and provide mechanism designers with all possible choices which meet the kinematic specifications. In contrast to other local numerical schemes such as Newton method and Powell method which are sensitive to initial guess, continuation method is a global convergence method that guarantee to find all solutions to the equations. In this paper, the problems with four and five precision points will be formulated, solved, and compared with the past results. We use the concept of graphical inversion and pole method to derive the design equations. Equations derived from such method are relatively simple. The total degree of the design equations is lower than other methods. Hence we may solve the design problems effectively. A reliable computer code using the numerical scheme has been developed and applied. The resulting mechanisms will be classified by their rotatability, and mechanisms with circuit and order defects will be examined.
"Complete Solution of the Five-Position Synthesis for Spherical Four-Bar Mechanisms,"
Journal of Marine Science and Technology: Vol. 6:
1, Article 3.
Available at: https://jmstt.ntou.edu.tw/journal/vol6/iss1/3