Kwun-Lon Ting

The effects of joint clearance on position and orientation deviation of linkages and manipulators

The paper presents a novel and simple approach to identify the worst position and direction errors due to the joint clearance of linkages and manipulators. It shows and proves that in a single loop linkage, joint clearances with the same value contribute equally to the direction deviation, and when used as a manipulator, the position error due to the joint clearance is always within an area enclosed by two four-bar coupler curves and two circular arcs. The method offers a geometrical model to explain and assess the output position or direction variation, to predict the limit of position uncertainty, to determine the maximum clearance, and hence to warranty the safety or precision of a mechanism. It can be used directly in any single closed loop linkage or manipulator and can also be extended to some multiloop linkages.

Uncertainty analysis of planar and spatial robots with joint clearances

Joint clearance in mechanisms and robots leads to uncertainty in function deviation. Unlike the effect of the link tolerance on the performance quality, the uncertainty effect of the joint clearance to the performance can not be eliminated by calibration because of the random nature. In this paper, based on the probability theory, a general probability density function (p.d.f.) of the endpoint of planar robots is established. The p.d.f. of the endpoint of a planer robot is equivalent to that of endpoint of a string of planar joint deviation vectors. By grouping the planar joint deviation vectors and establishing the structural constraint conditions between the vector groups, a basic approach of deriving the general p.d.f. of spatial robots is also presented. Based on the general p.d.f. of the endpoint, the distribution functions of the robot endpoint for any position tolerance zone and any joint distribution type, can be derived. The method is demonstrated by using some common types of position tolerance zones with uniform as well as normal distribution for joint clearance. The distribution functions of the robot endpoint are calculated and tabulated. These distribution functions and tables provide a convenient way to obtain the probability value for a robot to position its end point within a desired tolerance zone, and to determine the joint clearance value for the desired type of tolerance zone and the prescribed probability value of position repeatability.

Performance Quality and Tolerance Sensitivity of Mechanisms

This paper presents a general theory to determine the sensitivity of tolerances to the performance quality of mechanisms and a technique to identify a robust design, which is the least sensitive to the tolerances. The method is demonstrated in position synthesis of linkages. The sensitivity Jacobian is first introduced to relate the performance tolerances and the dimensional tolerances. The Rayleigh quotient of the sensitivity Jacobian, which is equivalent to Taguchis signal to noise ratio, is then used to define the performance quality and a sensitivity index is introduced to measure the sensitivity of the performance quality to the dimensional tolerances for the whole system. The ideal tolerance distribution is obtained in closed form. It shows how the tolerance specification affects the performance quality and that the performance quality can be significantly improved by tightening a key tolerance while loosening the others. The theory is general and the technique can be adapted easily for other mechanical systems, including multiple-loop linkages.

Topological Synthesis of Compliant Mechanisms Using Spanning Tree Theory

This paper introduces the spanning tree theory to the topological synthesis of compliant mechanisms, in which spanning trees connect all the vertices together using a minimum number of edges. A valid topology is regarded as a network connecting input, output, support, and intermediate nodes, which contains at least one spanning tree among the introduced nodes. Invalid disconnected topologies can be weeded out if no spanning tree is included. No further deformation analysis and performance evaluation is needed to invalidate disconnected topologies. Problem-dependent objectives are optimized for topological synthesis of compliant mechanisms. Constraints about maximum input displacement and force, maximum stress and overlapping connections are directly imposed during optimization process. The discrete optimization problem is solved by genetic algorithm with penalty function handling constraints. Two examples are given to verify the effectiveness of the proposed synthesis procedure.

Shape and Size Synthesis of Compliant Mechanisms Using Wide Curve Theory

A wide curve is a curve with width or cross section. This paper introduces a shape and size synthesis method for compliant mechanisms based on free-form wide curve theory. With the proposed method, detailed dimensions synthesis can be performed to further improve the performance after the topology is selected. Every connection in the topology is represented by a parametric wide curve in which variable shape and size are fully described and conveniently controlled by the limited number of parameters. The shape and size synthesis is formulated as the optimization of the control parameters of wide curves corresponding to all connections in the topology. Problem-dependent objectives are optimized and practical constraints are imposed during the optimization process. The optimization problem is solved by the constrained nonlinear programing algorithm in the MATLAB Optimization Toolbox. Two examples are included to demonstrate the effectiveness of the proposed synthesis procedure.

Adjustable slider–crank linkages for multiple path generation

Abstract Adjustable slider–crank linkages are capable of generating multiple paths with a simple adjustment of the position of the slider guider. Little work has been done in the area of synthesis of adjustable four-bar linkages for continuous path generation, especially of adjustable slider–crank linkages. The path flexibility of adjustable slider–crank linkages is analyzed. The optimal synthesis model is set up based on the position structural error of the slider guider introduced in this paper, which can effectively reflect the overall difference between the desired and the generated paths, avoid the difficulty of selecting corresponding comparison points on the two paths, and can be calculated conveniently. A genetic algorithm is employed to seek the global optimal solution. The results of an optimal synthesis example verify the effectiveness of the proposed method.

SMA actuated compliant bistable mechanisms

This article introduces the concept, analysis, as well as the design of shape memory alloy (SMA) actuated compliant bistable mechanisms. Compliant bistable mechanisms and SMA linear actuators have noteworthy advantages. When they are combined, not only their advantageous characteristics are preserved, but also some disadvantages can be eliminated. Thus, comparing to a stand-alone SMA actuator, SMA actuated compliant mechanisms have the advantages of requiring no input to stay at the stable positions, high repeatability in positioning, lightweight and simple control. Complexity in analysis, design, and control of SMA actuators and other shortcomings of SMA actuators, such as short output stroke and small output force, are either eliminated or improved.

Configuration analysis of complex multiloop linkages and manipulators

The article offers a simple and efficient method to identify all possible configurations up to 29 types of basic kinematic chains containing up to four independent loops. Basic kinematic chains may be regarded as the basic building blocks of any complex planar linkage. Given the required inputs to any single or multiple degree of freedom linkage, the linkage can always be decomposed into a set of basic kinematic chains. Since the method is capable of identifying all possible configurations of these 29 basic kinematic chains, the article offers the most general and versatile method available so far for the analysis of any complicate linkage composed of these basic kinematic chains. The method can be automated by initiating it with a structure analysis and classification, which identifies the linkage type, the simplest way of coupling among loops, and the complexity of the linkage, and then activating an one-dimensional search algorithm. The search is efficient. It requires no initial guess and does not lead to an erroneous solution. The complexity of analyzing a multiloop linkage may be affected by the choice of the input joints. Using an alternative input joint may lead to different basic kinematic chains and ,therefore, different level of complexity or even different number of configurations. The paper also shows that the number of possible configurations corresponding to a set of inputs given to a multiloop linkage is equal to the product of the numbers of configurations of its basic kinematic chains.

Classification and branch identification of Stephenson six-bar chains

Abstract A Stephenson six-bar chain contains a four-bar loop and a five-bar loop, and its branch condition may be affected by the rotatability of both loops and the interaction between them. It may have up to six branches and its branch condition is far more complicated than that of a four-bar chain. In this article, the method to identify the effects of both loops on the rotatability of any Stephenson six-bar linkage and the algorithms to identify its branch condition are presented. The results resolve one of the most complicated and troublesome problems encountered in the finite position synthesis of Stephenson linkages. The proposed method is based on the rotatability of the common joints between the two loops and no coupler curve is used. The method is directly applicable to any type of Stephenson linkages regardless of whichever link is used as the input or fixed link. It is also valid for linkages containing prism joints. The algorithms are equally effective for path, motion, and function generation and also for any number of precision positions. Once the branch problem is resolved, other mobility problems, such as the full rotation, dead center positions, and the motion order, can be identified easily as in planar four-bar linkages.

Kinematic Fundamentals of Planar Harmonic Drives

This paper presents the kinematic model and offers a rigorous analysis and description of the kinematics of planar harmonic drives. In order to reflect the fundamental kinematic principle of harmonic drives, the flexspline of a harmonic drive is assumed to be a ring without a cup. A tooth on the flexspline is a rigid body, and the motion of the tooth is fully governed by the wave generator and the nominal transmission ratio of the harmonic drive. The proposed model depicts the flexspline tooth and the wave generator as a cam-follower mechanism, with the follower executing a combined translating and oscillating motion. With the rigid tooth motion obtained, the conjugate condition between the flexspline and the circular spline is determined, from which the conjugate tooth profile can be derived. In this paper, the motion is governed by geometry, and the flexibility of the flexspline only serves as a spring to maintain the contact between the cam and the follower. For any wave generator and any transmission ratio, the explicit expression of the conjugate condition is presented. For a given circular or flexspline tooth profile, the exact conjugate tooth profile can be obtained. The phenomenon of twice engagement is discussed for the first time.