Chi Feng Chang

Synthesis of adjustable four-bar mechanisms generating circular arcs with specified tangential velocities

This work proposes synthesis methods to design the mechanism that is adjustable for tracing variable circular arcs with prescribed velocities. The constraint equations and useful properties of the desired mechanism are derived by using the concept of cross-ratio. The desired mechanism can be a crank-rocker or a slider-crank mechanism. The coupler curve of the mechanism, if necessary, can be symmetrical to itself. The practical applications of the mechanism are also discussed.

Synthesis of spherical four-bar path generator satisfying the prescribed tangents at two cusps

Abstract Design equations for spherical four-bar linkages to trace a coupler curve with two prescribed cusps are derived in this study by using a special case of spherical Burmester curves. For the case in which the tangents at two cusps are also prescribed, an analytical method is proposed with the aid of the foregoing design equations associated with the concept of the spherical cross ratio and spherical Bobillier theorem. The proposed method is straightforward and quite useful for those cases in which the tangents at two cusps are neither on the same plane nor on parallel planes. Numerical examples are also provided for illustrating the entire technique.

On the break-ups of spherical centre- and circle-point curves of the PP-PP case

Abstract With a pole and two instant centres specified on a unit sphere, a geometrical construction is proposed to determine the spherical centre- and circle-points. The explicit equations of the corresponding spherical centre- and circle-point curves of the PP-PP case are thus obtained by using spherical trigonometry. All break-ups of these spherical centre- and circle-point curves are directly generated from the explicit equations. Through an exhaustive search, it was found that there are four kinds of degenerated curves, i.e. (1) two points and a great circle, (2) two spherical ellipses and a great circle, (3) three orthogonal great circles and (4) a sphere. Two design examples are presented.

Cross ratio in sphere geometry and its application to mechanism design

Abstract In this paper a cross ratio theory applied in sphere geometry and its application on the spherical mechanism is presented. By expanding the cross ratio concept in plane geometry, cross ratio is proved to be equally valid in sphere geometry. Then, an alternative form of spherical cross ratio is proposed. An application of spherical cross ratio for the design of spherical four-bar mechanisms is presented.

Kinematic synthesis of Watt-I mechanisms generating closed coupler curves with up to four cusps

Abstract The analytical methods employed for synthesizing the Watt-I mechanisms, which generate closed coupler curves with up to four cusps, are presented in this paper. The necessary conditions for a Watt-I mechanisms to generate a cusp are classified. Closed-form aolutions for synthesizing the mechanisms which generate up to three cusps and pass through up to three coupler positions are also proposed. The mechanism generating closed coupler curve with four cusps is synthesized by using an optimization technique.

Remarks on the motion of link in the dwell-position

Abstract It has been found that the path of every point on a moving plane has a cusp in the T-position of the second kind, which is in nature an instantaneous dwell-position. In this paper, cases which violate such a property are found, hence the motion of a moving plane in the vicinity of the instantaneous dwell-position is investigated. Interesting properties and their interrelationships are obtained, such as the number of consecutive contact points between the fixed polode and the moving polode, the paths of points on the moving plane, path tangent at the cusp, etc. The instant center of a link in the instantaneous dwell-position, in general, cannot be determined by the existing methods. However, based on the current properties, the instant center can be determined analytically. A geometric procedure presented here is able to determine the instant center of the stationary link of six-link mechanisms in the limit position.