Wen Miin Hwang

Computer-aided structural synthesis of planar kinematic chains with simple joints

Abstract This paper presents a straightforward approach for the computer-aided structural synthesis of planar kinematic chains with simple joints, which consists of systematic generation of possible contracted link adjacency matrices, detection of degenerate chains and identification of isomorphic chains. Based on the proposed algorithm, a computer program is developed such that the catalogues of planar kinematic chains with the given number of links and degrees of freedom can be synthesized automatically. The number of kinematic chains with up to 13 links are listed.

Linkage path code

Abstract This paper presents the idea of linkage path code for the identification and recognition of planar kinematic chains with simple joints and turning pairs. For every given chain, this code can be obtained according to the definition directly or by a proposed method which can greatly simplify the procedures for obtaining the code by inspection.

Spherical four-bar linkages with symmetrical coupler-curves

In this paper we present analogies between planar and spherical four-bar linkages with symmetrical coupler-curves. Three types of planar four-bar linkages with symmetrical coupler-curves are investigated. For spherical linkages in contrast to these planar four-bar linkages, two types of them generate symmetrical coupler-curves, and so does the remaining one if it has special dimensions.

Optimal Synthesis of the Adjustable Knock-Out Cam-Follower Mechanism of a Bolt Former

Abstract This paper presents a feasible method for improvements to the adjustable knock-out cam-follower mechanism of a bolt former. On the basis of the results of analysing an existing knock-out mechanism of a bolt former, the design requirements for a new mechanism are developed. In order to meet some specific requirements and that the displacement, velocity, and acceleration curves of the follower motion are continuous, the new cam profile consists of two circular arcs and a fifth-degree or sixth-degree polynomial segment. For the cam profile with a sixth-degree polynomial segment, besides the six specified boundary conditions, a variable condition is used as a design variable for the optimization design. The maximum strike velocity between the knock-out screw and knock-out pin for all knock-out strokes is minimized by using the golden section method. The kinematic characteristics of the new knock-out camfollower mechanism synthesized are better than those of the existing mechanism. The method presented is illustrated by an example.

Defect-free synthesis of Stephenson-III motion generators

The main purpose of this article is to present a method for the dimensional synthesis of Stephenson-III motion generators without order, circuit, and branch defects. Using the concepts of the coupler curve of a four-bar linkage, the accessible region of a dyad, and the geometric feature of dead-centre configurations, a procedure is proposed for identifying the different circuits and branches of a Stephenson-III mechanism. Using the characteristics of order, circuit, and branch defects, the constraint equations to avoid them are presented. An optimization approach is proposed for the dimensional synthesis of defect-free Stephenson-III motion generators. An example is given to demonstrate the feasibility of the proposed method.

Coordination of two crank angles and two acceleration poles for a slider crank mechanism using parametric equations

The current article presents the parametric equations for the synthesis of a slider crank mechanism with a coupler point passing through two specified acceleration poles that accord with two specified crank angles. The parametric equations for the coordinates of the acceleration pole for the coupler with respect to the frame are shown to be functions of only the geometric configuration of the slider crank mechanism driven by the crank with a constant rotational speed. Moreover, a necessary condition for the crank angular interval corresponding to the two acceleration poles on a coupler curve generated by a slider crank mechanism is investigated. The desired coupler point of a given mechanism passing through two acceleration poles should be a double point on the locus of the acceleration pole described on the coupler plane. The transformed parametric equations on the fixed plane are then applied to synthesize the desired mechanism with a coupler point passing through two specified acceleration poles that accord with two specified crank angles.

Synthesis of planar five-bar pantograph configurations by a geometric method

We present a geometric method for structural synthesis of planar five-bar pantograph configurations. Based on the concept of similarly varying triangles, the geometric conditions for a five-bar linkage to be a pantograph are derived according to a complex number approach. Under these conditions, a geometric procedure is proposed to synthesize all five-bar pantograph configurations with four or three similarity points systematically. In total 13 configurations with four similarity points and 23 configurations with three similarity points are obtained. The results of this work provide a complete atlas of pantograph configurations superior to existing ones.

Synthesis of a Six-Coaxial-Link Planetary Gear Train for Seven-Speed Automatic Transmissions

This paper presents a methodology for the kinematic synthesis of seven-speed automatic transmissions with a two-degree-of-freedom and six-coaxial-link planetary gear train. A detection proof is used to filter out unsuitable planetary gear trains for seven-speed automatic transmissions. A six-coaxial-link compact planetary gear train with three mutually meshed planet gears is selected as the design target. Based on the requirements for clutch-to-clutch shifts and decreasing speed ratios, an existing algorithm is used to generate feasible clutching sequences. An exhaustive searching method for the optimum numbers of teeth on gears is used to minimize the differences between the set of desired speed ratios and that of generated speed ratios. The ten best combinations of the numbers of teeth on gears for each clutching sequence are then found. Finally, the mechanical efficiencies of the ten sets are calculated for evaluation. Six valid configurations with only six clutches are obtained for seven-speed automatic transmissions.

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.