Long-Iong Wu

Mathematical model and undercutting analysis of elliptical gears generated by rack cutters

The theory of gearing and geometry of the straight-sided rack cutter are employed to develop a mathematical model of elliptical gears that takes backlash into consideration. The mathematical model also includes the bottom land of the elliptical gear, which is equidistant from the pitch ellipse. A computer program is developed to generate the tooth profile of elliptical gears. The profile of elliptical gears obtained by applying the proposed method is compared with that obtained by the evolute method. Undercutting of elliptical gears is also investigated. The results of this research should be helpful in the design, manufacture, and measurement of elliptical gears. Copyright 1996 Elsevier Science Ltd

Mechanical Error Analysis of Disk Cam Mechanisms with a Flat-Faced Follower

By employing the concept of equivalent linkage, this paper presents an analytical method for analyzing the mechanical errors of disk cam mechanisms with a flat-faced follower. The resulting error equations do not really involve the location of the curvature center of the cam profile, and locating the curvature center of the cam profile is not essential. The resulting errors are significantly affected by the pressure angle, and the smaller pressure angle will result in the smaller mechanical error. In the worst case, owing to the joined effects of various design parameters, the accuracy of the follower motion may degrade considerably. For the oscillating follower case, all acceleration error functions have a sudden change at every beginning and at every end of the motion even though the theoretical follower displacement is cycloidal motion.

A Simplified Method for Examining Profile Deviations of Conjugate Disk Cams

The profile errors of conjugate disk cams can be indirectly examined by means of measuring the conjugate condition of the assembled conjugate cam mechanism. This paper demonstrates how to measure the conjugate condition of the assembled conjugate cam mechanism to reveal the cam profile errors and also develops an analytical approach for relating the variation of the conjugate condition with the cam profile errors. For the machined conjugate cams with profile errors, if the subtending angle of the oscillating follower arms is intentionally changed to be variable, the variation of the subtending angle of the follower arms may indicate the variation of profile errors when the cams rotate. According to the magnitude of the subtending angle variation, the profile deviations of conjugate disk cams can be analyzed analytically. The profile errors of a pair of conjugate cams can be evaluated by means of the corresponding motion variation of the indicator reading. For such an examining method, the only required measuring instrument is a dial indicator. A pair of conjugate cams were examined by the method and also measured using a coordinate measuring machine to test the accuracy and efficiency of the method.

Creative mechanism design for a prosthetic hand.

Abstract In this paper, an auxiliary methodology called the creative mechanism design is introduced into the innovation of gripping devices for prosthetic hands. This methodology is a systematic approach based on modification of existing devices for the generation of all possible topological structures of mechanisms and mechanical devices. An existing gripping device (Teh Lin ATG-5F prosthetic hand) constructed by a planar six-bar linkage with one degree of freedom is dealt with by using this methodology. Through the processes of generalization, number synthesis, specialization and particularization for the existing design, five new mechanisms are created in this study to apply to anthropomorphic prosthetic hands. The results show that the methodology for creative mechanism design is a powerful tool for creating new categories of mechanisms to avoid existing designs that have patent protection and can help designers in the conceptual phase. Also, this methodology is validated as a useful way to improve prosthetic hands for amputees.

Inspecting Profile Errors of Conjugate Disk Cams With Coordinate Measurement

To inspect cam profile errors, a coordinate measuring machine (CMM) is frequently employed. The coordinate data of discrete points at the cam surface are measured by a CMM in order to further evaluate the actual cam profile with complicated interpolation algorithms, and then the cam contour approximated by these algorithms may be compared with the theoretical one. In this paper, a direct and simple analytical method, instead of a numerical interpolation algorithm, is proposed for inspecting the profile deviations of conjugate disk cams with coordinate measurement data. The method is based on the derived correlation between the radial-dimension errors and the normal-direction errors of conjugate cam profiles. To verify the proposed method, an experiment of inspecting a pair of conjugate disk cam profiles was conducted. The experimental results obtained from the proposed method were compared with those obtained by using the Hermite interpolation method. It shows that this method is accurate and more efficient for inspecting the profile errors of conjugate disk cams.

Computerized tolerance analysis of disk cam mechanisms with a roller follower

The tolerance analysis is one of the key elements of design and manufacturing of cam mechanisms. This paper presents a computerized method for analyzing the tolerances in disk cam mechanisms with a roller follower. By employing the concept of simulated higher-pair contact analysis, the kinematic deviation of the follower motion arising from the tolerance amount of each design parameter can be determined numerically. The offset translating roller follower and the oscillating roller follower cases are given to illustrate the proposed method. The tolerance analysis results show that, owing to the combined effects of various design parameters, the position accuracy of the follower motion may degrade considerably. But, the tolerance amounts of the design parameters may also have a compensating effect to enhance the relative accuracy of the follower motion between its high and low dwell positions. Hence, it is possible to find the optimal tolerance combination for balancing the kinematic accuracy and the tolerance amounts of disk cam mechanisms with a roller follower.

Simplified graphical determination of disk-cam curvature

Abstract The equivalent four-bar linkage of a disk-cam mechanism can be constructed through the application of Freudenstein’s third theorem if the kinematic characteristics of the follower instead of the profile of the disk cam are specified. From such a process of reversing the usual construction order, the instantaneous radius of curvature of a disk-cam profile can be determined by means of the joint locations of the equivalent linkage. Based on this process, this paper presents a simple graphical method for determining the radius of curvature of a disk-cam profile. For most cases, the results obtained from this method are reasonably accurate.

Tolerance analysis and synthesis of cam-modulated linkages

Abstract Cam-modulated linkages that can achieve superior kinematic performance as compared with pure linkages have been widely applied in a variety of automation machinery. The tolerance analysis and synthesis are thus quite essential in the design and manufacture of precision cam-modulated linkages. This paper presents comprehensive and systematic mathematical tools for dealing with the tolerance analysis and synthesis of cam-modulated linkages. Based on the concept of equivalent linkage and the derived correlation between the radial-dimension errors and the normal-direction errors of the cam profile, the sensitivity analysis method for equivalent linkages is introduced for analyzing the tolerances in cam-modulated linkages, whose output error equations can be derived through an analytical means. Then, by incorporating the sensitivity analysis method and the concept of design for manufacturing and assembly (DFMA), an optimization model for synthesizing the tolerances in cam-modulated linkages is developed. The objective of this optimization model is to maximize the manufacturability and assembility of a cam-modulated linkage while maintaining acceptable kinematic accuracy of its output motion. A practical case study of analyzing and synthesizing the tolerances in a cam-modulated linkage type pick-and-place device is then performed to illustrate the presented methods. It shows that the mathematical tools presented can be helpful to the design and manufacture of precision cam-modulated linkages.

Conceptual Innovation of a Prosthetic Hand Using TRIZ

Planar linkages with one degree of freedom have been applied to prosthetic hands in the past years, but only one gripping configuration can be performed by these designs. This paper demonstrates the conceptual design processes for a patented prosthetic hand, which has the functions for switching the gripping forms and locking the gripping configuration. A systematically innovative methodology called the Theory of Inventive Problem Solving (TRIZ) is employed to generate the concepts for the desired functions. The skills of Contradiction and Substance-Field Analysis in TRIZ are effectively applied in this study. Also, motion simulation for an embodiment of the proposed prosthetic hand is given by using the Working Model(superscript ®) 3D software. The simulating results show that the design is applicable to perform two different gripping forms for hand prostheses.

A note on Freudenstein's theorem

In this paper analytical expressions for the extreme velocity ratio of a four-bar linkage are derived by the application of vector loop equations. Alternative forms for Freudensteins theorems are presented. Either geometrically or analytically, the theorems can be proved concisely. For an arbitrary four-bar linkage, Freudensteins theorem can examine the occurrence of the phases at which the angular velocity ratio of links becomes extreme, but it cannot straightforwardly determine the exact phases to happen.