bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Skeleton of Simple CSG Objects
Authors: Dutta D. , Hoffmann C. M.
Published: June 2008

The skeleton (medial-axis surface) of an object is the locus of all points in the object’s interior that have equal minimum distance from at least two distinct parts of the boundary. The skeleton can be used in blending, motion planning, medical tomography, computer vision, and in mesh generation. We discuss some simple but frequently encountered shape elements of the skeleton of CSG objects, and investigate properties of trimming surfaces delimiting the faces of skeletons.
Computation of Spatial Displacements From Geometric Features
Authors: Ravani B. , Ge Q. J.
Published: June 2008

This paper develops the theoretical foundation for computations of spatial displacements from the simple geometric features of points, lines, planes, and their combinations. Using an oriented projective three space with a Clifford Algebra, all these three features are handled in a similar fashion. Furthermore, issues related to uniqueness of computations and minimum number of required features are discussed. It is shown that contrary to the common intuition, specification of a minimum of four points (planes) or three lines are necessary for computation of a unique displacement. Only when the sense of the orientations of these features are specified then the minimum number of required features reduces to three for points and planes and two for lines. The results, in addition to their theoretical interest in computational geometry of motion, have application in robot calibration.
Workspace Boundaries of Free-floating Open and Closed Chain Planar Manipulators
Authors: Agrawal Sunil Kumar , Garimella Rao
Published: June 2008

It is well known that workspace of fixed-base manipulators is dependent on the geometry of its links. This paper presents studies on the workspace of free-floating manipulators. A unique property of free-floating manipulators is that the workspace is not only a function of links’ geometry but is also dependent on the mass distribution. This paper addresses the question of how to find the workspace and boundaries of free-floating open and closed-chain planar manipulators. Further, the effect of mass distribution on the workspace of the manipulator is studied and guidelines for design of the manipulator are suggested.
Numerical Analysis of the Kinematic Working Capability of Mechanisms
Authors: Yang Feng-Cheng , Haug E. J.
Published: June 2008

A broadly applicable approach for numerical analysis of the kinematic working capability of mechanisms is presented. Composite workspaces are introduced to represent position and orientation capabilities of mechanisms, both individually and together. Numerical methods for solving systems of kinematic constraint equations, using a moving-frame algorithm and equations that characterize the workspace boundary are developed. Two analytic methodologies, comparison and incorporation methods, are presented to determine whether the workspace of a mechanism satisfies design requirements. An experimental computer program for workspace analysis that incorporates a numerical solver and computer graphics for visualization on a high speed graphics workstation is outlined. The feasible positioning space of a Stewart platform that is subject to orientation constraints is computed, to illustrate the use of this approach.
Numerical Analysis of the Kinematic Dexterity of Mechanisms
Authors: Yang Feng-Cheng , Haug E. J.
Published: June 2008

A general approach to numerical analysis of the kinematic dexterity of mechanisms is presented. Dextrous workspace problems are first defined and illustrated with examples. Composite workspaces are introduced to characterize both positioning and orienting capabilities of mechanisms. A numerical formulation and computer implementation that incorporates computer graphics and a numerical algorithm for solving systems of nonlinear equations are presented. Using the composite workspace formulation and the computer implementation, numerical techniques for dextrous workspace analysis are presented. Examples are given to illustrate the techniques developed.
Repeatable Joint Displacement Generation for Redundant Robotic Systems
Authors: Chung Y. S. , Griffis M. , Duffy J.
Published: June 2008

This paper presents a novel, practical, and theoretically sound kinematic control strategy for serial redundant manipulators. This strategy yields repeatability in the joint space of a serial redundant manipulator whose end effector undergoes some general cyclic type motion. This is accomplished by deriving a new inverse kinematic equation that is based on springs being theoretically or conceptually located in the joints of the manipulator (torsional springs for revolute joints, translational springs for prismatic joints). Previous researchers have also derived an inverse kinematic equation for serial redundant manipulators. However, to the authors’ knowledge, the new strategy is the first to include the free angles of torsional springs and the free lengths of translational springs. This is important because it ensures the repeatability in the joint space of a serial redundant manipulator whose end effector undergoes a cyclic type motion. Numerical verification for repeatability is done in terms of Lie bracket condition. Choices for the free angle and torsional stiffness of a joint (or the free length and translational stiffness) are made based upon the mechanical limits of the joint.
An Energy-Based General Method for the Optimum Synthesis of Mechanisms
Authors: Avile´s R. , Navalpotro S. , Amezua E. , Herna´ndez A.
Published: June 2008

The aim of the present paper is to set forth a method for the optimum synthesis of planar mechanisms. The method in question can be applied in the case of any mechanism and kinematic synthesis (function, path generation, rigid-body guidance, or combination of these). The mechanisms are discretized with bar-finite elements that facilitate the computation of the geometric matrix, which is a stiffness matrix. The error function is based on the elastic energy accumulated by the mechanism when it is compelled to fulfill exactly the synthesis data. Thus during the iterative process the elements of the mechanism may be considered deformable. The energy computation for each synthesis datum requires the solution of the nonlinear equilibrium position. This problem is solved with the help of the geometric matrix and the force vector of the deformed system. The minimization of the error function is based on Newton’s method, with a semianalytic approach. Analytic and finite-difference concepts are used together in the calculation of the gradient vector and of the second-derivative matrix. The method has proved very stable for a wide range of step sizes. There is convergence to a minimum even when the start mechanism is far from a solution. Examples with different mechanisms and syntheses are also provided.
The Transmissivity and Manipulability of Spatial Mechanisms
Authors: Tsai M. J. , Lee H. W.
Published: June 2008

A method of evaluating the transmission performance for spatial mechanisms is developed using the reciprocity of screws. The actual transmission performance of a spatial mechanism should be composed of two parts: the ability of the output that can be effectively generated by the mechanism is called the “transmissivity,” and the ability of the input that can be effectively absorbed into the rest part of the mechanism is called the “manipulability.” A more generalized index for the overall transmission performance of spatial mechanisms is then defined and illustrated by some spatial four-link mechanisms.
A Unified Theory for Kinematic Synthesis
Authors: James P. A. , Roth B.
Published: June 2008

In this paper we derive an analytic method for obtaining infinitesimal kinematic synthesis results as a limiting process from finitely-separated position kinematics. Expanding on previous work, we extend the unified theory to include spatial kinematic synthesis and we present a new numerical method. The new methods serve to unity finite, infinitesimal, and hybrid kinematic synthesis into one theory for kinematic synthesis.
Position-Force Synthesis of Closed-Loop Linkages
Authors: Huang C. , Roth B.
Published: June 2008

The dimensional synthesis of spatial closed-loop linkages to match both force and position specifications is investigated. An efficient means of formulating force equations is introduced through the application of linear algebra to screw theory. The synthesis of spatial four-bar linkages is discussed in detail; it is shown that the maximum number of allowable design positions is not decreased after force constraints are imposed on classical position synthesis problems.
Simplified Equations for the Synthesis of Four-Bar Path Generator With Specified Tangents at Two Cusps
Authors: Hwang Wen-Miin , Chang Chi-Feng
Published: June 2008

An analytical method for the synthesis of planar four-bar path generator with specified inclinations of path tangents at two cusps has been presented here. Simplified equations based on the concept of kinematic inversion and cross-ratio have been derived for the design problem. The desired four-bar linkages have been synthesized directly by using these analytical equations.
Optimization of a Spherical Five-Bar Parallel Drive Linkage
Authors: Ouerfelli M. , Kumar V.
Published: June 2008

The spherical five bar parallel drive linkage is investigated for use as a spherical manipulator or as a pointing mechanism. The direct and inverse kinematics are derived for a general 5-R linkage. Kinematic and dynamic optimization yields a geometry in which all link lengths are equal to a right angle.
Analysis and Optimal Synthesis of the RSCR Spatial Mechanisms
Authors: Ananthasuresh G. K. , Kramer S. N.
Published: June 2008

A closed form solution of the analysis of the RSCR (Revolute-Spherical-Cylindrical-Revolute) spatial mechanism is presented in this paper. This work is based on the geometric characteristics of the mechanism involving the following three cases: the cone, the cylinder, and the one-sheet hyperboloid. These cases derive their names from the nature of the locus of the slider of the linkage as viewed from the output side. Each case is then treated separately to develop a closed form, geometry based analysis technique. These analysis modules are then used to optimally synthesize the mechanism for function, path and motion generation problems satisfying precision conditions within prescribed accuracy limits. The Selective Precision Synthesis technique is employed to formulate the nonlinear inequality constraints. These constraints along with an objective function and other constraints are solved using the Generalized Reduced Gradient method of optimization. In addition, mobility charts are used to aid the designer in making a judicious choice for the initial design point before invoking the optimization method. Numerical examples are presented to validate the theory. This new closed form method of analysis that is based on geometric characteristics is computationally less intensive than other available techniques for spatial mechanism analysis and helps in the visualization of the physical mechanism; something that is not possible with most vector and matrix methods.
The Kinematic Control Equations of a Singularity-Free Six-Degree-of-Freedom Manipulator
Authors: Di Caprio F. , Stanisˇic´ M. M.
Published: June 2008

In this paper, one symmetrically actuated double pointing system is used in the shoulder subassembly, and another is used in the wrist subassembly of a six-degree-of-freedom manipulator. In a previous paper, this manipulator was shown to be free of singularities. In this paper, the position control equations are derived.
On Identification and Canonical Numbering of Pin-Jointed Kinematic Chains
Authors: Shin Jae Kyun , Krishnamurty S.
Published: June 2008

This paper deals with the development of a standard code for the unique representation of pin-jointed kinematic chains based on graph theory. Salient features of this method include the development of an efficient and robust algorithm for the identification of isomorphism in kinematic chains; the formulation of a unified procedure for the analysis of symmetry in kinematic chains; and the utilization of symmetry in the coding process resulting in the unique well-arranged numbering of the links. This method is not restricted to simple jointed kinematic chains only, and it can be applied to any kinematic chain which can be represented as simple graphs including open jointed and multiple jointed chains. In addition, the method is decodable as the original chain can be reconstructed unambiguously from the code values associated with the chains.
Development of a Standard Code for Colored Graphs and Its Application to Kinematic Chains
Authors: Shin Jae Kyun , Krishnamurty S.
Published: June 2008

The development of an efficient solution procedure for the detection of isomorphism and canonical numbering of vertices of colored graphs is introduced. This computer-based algorithm for colored graphs is formed by extending the standard code approach developed earlier for the canonical numbering of simple noncolored graphs, which fully utilizes the capabilities of symmetry analysis of such noncolored graphs. Its application to various kinematic chains and mechanisms is investigated with the aid of examples. The method never failed to produce unique codes, and is also found to be robust and efficient. Using this method, every kinematic chain and mechanism, as well as path generators and function generators, will have their own unique codes and a corresponding canonical numbering of their respective links. Thus, based on its efficiency and applicability, this method can be used as a universal standard code for identifying isomorphisms, as well as for enumerating nonisomorphic kinematic chains and mechanisms.
Analysis of Errors in Precision for Closed Loop Mechanisms
Authors: Lin Psang Dain , Chen Jen Fun
Published: June 2008

An algorithm to analyze the relations of error components for closed loop mechanisms is introduced. The error components considered are errors in link dimensions and error motions due to joint clearances. In order to completely characterize the physical shape of a link, first a revision of the Denavit-Hartenberg symbolic notation is introduced. Then, an error matrix is proposed to account for the effects of error motions due to joint clearances. Six independent equations are obtained. The major benefit from these equations is the capability of assessing the influence of each error component on a machine’s accuracy. This analysis is particularly useful to allocate a machine’s tolerances at its design stage and to characterize the performance of an existing machine.
Errors in Constant-Velocity Shaft Couplings
Authors: Fischer I. S. , Remington P. M.
Published: June 2008

Shaft couplings with an odd number of joints are modeled with rotation matrices such that the transmission plane in which the axis of the central joint moves can be arbitrarily specified. It is shown that when the transmission plane coincides with the homokinetic plane, the mechanism functions as a constant velocity coupling, otherwise it does not. The cyclic variation in output speed, which occurs when the constant-velocity criteria is not met, is quantified and the results enable the design engineer to predict performance of constant-velocity couplings when deviation from ideal geometry occurs because of manufacturing and installation tolerances or wear.
Instantaneous Kinematics of a Tangent-Plane in Two-Parameter Space Motion
Authors: Sathyadev D. P. , Soni A. H.
Published: June 2008

A tangent-plane undergoing two-parameter motion envelopes a surface called the tangent-plane envelope. Such surfaces can be considered as the envelope of a two-parameter family of planes or ∞2 family of planes. The properties of the tangent-plane motion are characterized through the properties of the spherical image of the normal to the surface it envelopes. This paper presents a methodology to locate a family of planes that envelope surfaces with similar characteristics.
Assembling Complete Pole Configurations for (Over)Constrained Planar Mechanisms
Authors: Dijksman E. A.
Published: June 2008

The complete pole configuration of a planar n-link mechanism having one instantaneous degree of mobility, possesses (3n−4)/2 independent poles determining (n−2)2/2 remaining poles of the configuration. The dependency is demonstrated through Desargues’ Theorem and her generalizations. Simultaneously, pole configurations have been “elated” into three-dimensional point-lattices intersected by a plane. The insight obtained in these configurations allows the designer to find clues in building overconstrained linkage mechanisms meeting certain geometrical properties.
A Quintic Spline Interpolator for Motion Command Generation of Computer-Controlled Machines
Authors: Yang D. C. H. , Wang Fu-Chung
Published: June 2008

This paper presents a new method of motion command generation for computer controlled multi-axis machines. The method is based on a quintic spline interpolator (QSI) which generates motion commands to trace a set of desired discrete position data via a composite quintic spline (CQS). This CQS is nearly arc length parametrized and has second order continuous at the data points. Consequently, the generated motion trajectories are continuous in both velocity and acceleration throughout the motion. A quick motion command generation scheme is also developed. Compared to the existing linear interpolator (LI), the proposed method takes comparable execution time, but is superior in many other aspects, including position accuracy, speed smoothness, acceleration continuity, torque requirement, and jerk reduction. Compared to the existing cubic spline interpolator (CSI), the proposed method is able to maintain a similarly smooth composite profile, but better speed accuracy. On-line implementation of this interpolator is believed very promising.
Motion Conversion by Means of Perturbation of Elastic Field
Authors: Xu Huang Da
Published: June 2008

In this paper a new principle of motion conversion is described. Mechanisms based on this principle are used to convert variable low amplitude oscillatory motions into smooth continuous rotary or straight line motions. Application of this principle to implement a high performance piezoelectric motor is described together with some variations. The working cycle of the piezoelectric actuators in the piezoelectric motor is analyzed showing energy density of the actuators on an order of magnitude higher than in conventional use. Another application to implement a torque-limited speed-reducer is also described.
The Elastic-Dynamic Modeling of a Press Feed Mechanism
Authors: Chassapis C. , Lowen G. G.
Published: June 2008

The development of a mathematical model, describing the elastic-dynamic response of an industrial lever type roll feed mechanism, is presented. This device, which is used in all manner of powerpress work, consists of an RSSR linkage with a bent coupler, an indexing-type sprag clutch, a set of feed and pressure rollers, which move a metal strip into a die, and a disc brake. Its intermittent motion has been characterized by four motion regimes. While the spatial coupler link is considered to have distributed mass and electricity, the clutch model neglects the masses of the sprags and represents the total clutch elasticity by way of a single, nonlinear, massless torsional spring. The derivation of the equations of motion of the coupler and the feed-roller driven metal strip, for the various regimes, is based on Hamilton’s principle. The subsequent application of the method of Kantorovich, wherein the space portions of the coupler motion are expressed in terms of its in and out-of-plane free-vibration modes, makes it possible to obtain coupled ordinary differential equations for the feed-roller motion, as well as the time portions of the coupler deflections.
Computer Simulation of a Press Feed Mechanism and Experimental Confirmation
Authors: Chassapis C. , Lowen G. G.
Published: June 2008

An experimentally verified simulation of the elastic-dynamic behavior of a lever-type feed mechanism is presented. Based on a combination of experimental and analytical findings, simplified motion equations could be introduced. In the experimental set-up, the motion of the mechanism is monitored by three angular encoders, which are attached to the drive shaft, the rocker-link shaft, and the feed roller shaft, respectively. Their output, which is stored in a specially designed data acquisition system, allows the correlation of the instantaneous rotations of the feed roller and the rocker shafts to that of the drive shaft. Strain gages provide in and out-of-plane bending-strain histories of the bent coupler. Experiment and theory, for different loading conditions, are correlated by way of the coupler strain, the clutch windup angle and the total feed length. Good qualitative and quantitative agreement between computed and experimental results was found.
A New Damping Model for Nonlinear Stiffness Systems With Variable Preload Displacements and Constant Amplitude Decay Ratios
Authors: Xu T. , Lowen G. G.
Published: June 2008

This study of the behavior of nonlinear stiffness systems with variable preload displacements and constant amplitude decay ratios showed that the energy loss per cycle is dependent on these preload displacements. By introducing a nonlinear damping force, which is a function of both displacement and velocity, the associated work per cycle can be made approximately the same function of the preload displacement as is the case for the energy loss. In this manner, it becomes possible to make the resulting damping coefficient essentially independent of the preload displacement. This new damping model was incorporated into the mathematical description of an over-running sprag clutch. Confirming experimentation showed very good agreement with computed results.
Steady-State Responses of an RSRC-Type Spatial Flexible Linkage
Authors: Chang R. Y. , Sung C. K.
Published: June 2008

This paper presents an analytical and experimental investigation on the steady-state responses of an RSRC-type spatial flexible linkage. The kinematic analysis of the spatial rigid-body motion is performed using kinematic constraint equations to yield the linear and angular positions, velocities, and accelerations of the linkage. A mixed variational principle is, then, employed to derive the equations of motion governing the longitudinal, transverse, and torsional vibrations of the flexible link and the associated boundary conditions. Based on these equations, the steady-state responses are predicted. Finally, an RSRC-type four-bar spatial flexible linkage is constructed and the experimental study is performed to examine the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.
A Method for the Design of Compliant Mechanisms With Small-Length Flexural Pivots
Authors: Howell L. L. , Midha A.
Published: June 2008

Compliant or flexible-link mechanisms gain some or all of their motion from the relative flexibility of their joints rather than from rigid-body joints only. Unlike rigid-body mechanisms, energy is not conserved between the input and output ports of compliant mechanisms because of energy storage in the flexible members. This effect and the nonlinearities introduced by large deflections complicate the analysis of such mechanisms. The design of compliant mechanisms in industry is currently accomplished by expensive trial and error methods. This paper introduces a method to aid in the design of a class of compliant mechanisms wherein the flexible sections (flexural pivots) are small in length compared to the relatively rigid sections. The method includes a definition and use of a pseudo-rigid-body model, and the use of a large-deflection finite element type algorithm. An example is used to illustrate the design technique described.
Determination of the Optimum Cost-Residual Error Trade-off in Robot Calibration
Authors: Zak G. , Fenton R. G. , Benhabib B.
Published: June 2008

Most industrial robots cannot be off-line programmed to carry out a task accurately, unless their kinematic model is suitably corrected through a calibration procedure. However, proper calibration is an expensive and time-consuming procedure due to the highly accurate measurement equipment required and due to the significant amount of data that must be collected. To improve the efficiency of robot calibration, an optimization procedure is proposed in this paper. The objective of minimizing the cost of the calibration is combined with the objective of minimizing the residual error after calibration in one multiple-objective optimization. Prediction of the residual error for a given calibration process presents the main difficulty for implementing the optimization. It is proposed that the residual error is expressed as a polynomial function. This function is obtained as a result of fitting a response surface to either experimental or simulated sample estimates of the residual error. The optimization problem is then solved by identifying a reduced set of possible solutions, thus greatly simplifying the decision maker’s choice of an effective calibration procedure. An application example of this method is also included.
Evaluation of Parametric Vibration and Stability of Flexible Cam-Follower Systems
Authors: Mahyuddin A. I. , Midha A. , Bajaj A. K.
Published: June 2008

A method to study parametric stability of flexible cam-follower systems is developed. This method is applied to an automotive valve train which is modeled as a single-degree-of-freedom vibration system. The inclusion of the transverse and rotational flexibilities of the camshaft results in a system governed by a second-order, linear, ordinary differential equation with time-dependent coefficients. This class of equations, known as Hill’s equations, merits special notice in determination of the system response and stability. The analysis includes development of the equivalent model of the system, derivation of its equation of motion, and a method to evaluate its parametric stability based on Floquet theory. A closed-form numerical algorithm, developed to compute the periodic response of systems governed by second-order, linear, ordinary differential equations of motion with time-dependent coefficients, is utilized. The results of this study are presented in a companion paper in the forms of parametric stability charts and three-dimensional stability and response charts.
Influence of Varying Cam Profile and Follower Motion Event Types on Parametric Vibration and Stability of Flexible Cam-Follower Systems
Authors: Mahyuddin A. I. , Midha A.
Published: June 2008

A method to study parametric stability of flexible cam-follower systems, based on Floquet theory, as well as a closed-form numerical algorithm to compute periodic response of the system, have been developed in a companion paper. These are applied to an automotive valve train, modeled as a single-degree-of-freedom vibration system. The inclusion of the transverse and rotational flexibilities of the camshaft results in a system that is governed by a linear, second-order, ordinary differential equation with time-dependent coefficients. In this paper, the parametric stability of the system is studied, and the results are presented in the form of parametric stability charts. The regions of instability are plotted on the nondimensionalized frequency and excitation (amplitude) parameter plane. The maximum positional error of the follower motion, analyzed by the closed-form numerical algorithm, enables a novel presentation of three-dimensional stability and response charts. Stability of the system is investigated for three types of follower motion events and four different cam profiles. The effect of damping on parametric instability is also studied. A comparative study of these event and cam profile types reveals some very interesting and hitherto unknown results.
The Design of Cam Mechanisms With Translating Flat-Face Followers Under Curvature Constraints
Authors: Angeles J. , Saha S. K. , Lo´pez-Caju´n C. S.
Published: June 2008

The optimization of cam mechanisms with translating flat-face followers, upon consideration of curvature constraints, is discussed here. When minimizing the size of the cam disk, cam profiles with cusps, i.e., profiles with curvature discontinuities, can appear. On the other hand, cusps are undesirable because they give rise to inadmissibly large contact stresses and hence, should be prevented from occurring. Conditions under which these discontinuities appear, although available in the literature, are not readily applicable to a specific problem. However, if the synthesis of the follower-displacement program is based on spline functions, then readily applicable design formulas, leading to unconstrained optimum designs, are derived. In the presence of curvature constraints, design charts are derived that produce the cusp-free, minimum-size profile for a given displacement program. The same problem for oscillating flat-face followers is addressed in an accompanying paper.
The Design Optimization of Cam Mechanisms With Oscillating Flat-Face Followers Under Curvature Constraints
Authors: Angeles J. , Saha S. K. , Gonzalez-Palacios M. , Lopez-Cajun C. S.
Published: June 2008

This paper follows an accompanying one on the constrained minimization of cam profiles with translating flat-face followers. Here, the corresponding problem for oscillating flat-face followers is discussed. The unconstrained optimization of this type of cam mechanisms, aimed at the minimization of the area of the cam disk, has been reported elsewhere. In this paper we recognize that unconstrained cam-size minimization can lead to profiles with curvature discontinuities, i.e., cusps, which should be eliminated, for they give rise to inadmissibly large contact stresses. The conditions under which curvature discontinuities arise are derived. These conditions lead to a simple constrained minimization procedure, whose application is illustrated with a fully solved numerical example.
Synthesis of Contact Surfaces of Spherical Cam-Oscillating Roller-Follower Mechanisms: A General Approach
Authors: Gonza´lez-Palacios M. A. , Angeles J.
Published: June 2008

A novel method of synthesis of the surface geometry of spherical cam-oscillating roll-follower mechanisms is introduced. The approach aims at zeroing the sliding velocity between the cam and the roller, their respective geometries being thus obtained as conical surfaces. The pressure angle is analyzed in detail. Specific results are presented for the application of this synthesis technique to indexing cam mechanisms.
Application of the Theory of Envelope to the Determination of Camoid Profiles With Translating Followers
Authors: Tsay Der Min , Hwang Guan Shyong
Published: June 2008

A new, simple procedure employing the theory of envelope for a family of surfaces with two independent parameters to determine the profiles of camoids with translating spherical followers is presented. Given the follower motion program, the method enables the kinematic relationship for the camoid surface coordinates to be easily generated in an analytical expression. The results are then compared to those obtained by utilizing the principle of contact point between the camoid and the follower surfaces. The pressure angle is analyzed, and the cutter paths required in the machining process are also produced. A numerical example is given to illustrate the application of the approach.
Signal Flow Graphs for Spatial Gear Trains
Authors: Ma R. , Gupta K. C.
Published: June 2008

Signal flow graphs (SFG) have been applied in many areas such as circuit analysis, controls, mechanical vibrations, statistics, and operations research. They have also been applied to the analysis of planetary gear trains which are planar, i.e., where all of the gear axes are parallel. In this paper, signal flow graphs are applied to spatial planetary gear trains. Some additional terminology and rules which are needed for this important application are developed in this paper and illustrated by examples. The significance of applying SFG to a gear system is that the graph describes the interrelationship among the system variables by linking causes and effects, offers the information about the topology of system connection, and the kinematic equations of motion can be written easily by inspection. In this way, it helps use to visualize and understand spatial gear train systems better.
Efficiency of a Multiple Flywheel Recuperation System
Authors: Marinov P. , Pavlov S. , Draganov V.
Published: June 2008

A multiple flywheel has been studied for the purpose of storing and recuperating kinetic energy. The objective of the design of such systems is a maximum storage and recuperation of the stored energy. Dynamic models of the proposed and the conventional systems are compared regarding energy losses. A coefficient of recuperating efficiency is introduced for demonstrating the advantages of the multiple flywheel system.
Recursive Formulation for the Inverse Kinematics of Redundant Robots Performing Tasks with Priority Order
Authors: Garziera R.
Published: June 2008

A recursive arrangement is given for the inverse kinematic differential equations of redundant robots performing tasks with priority order. This formulation leads to simple and easy-to-handle equations, particularly suitable to be implemented in computer algorithms, for any number of sub-tasks. Moreover the recursive structure is extended to the solution at the acceleration level.
Invariant Link Rotatability of N-Bar Kinematic Chains
Authors: Shyu J. H. , Ting Kwun-Lon
Published: June 2008

This paper proposes and proves the concept of invariant link rotatability between any two links, adjoined or not, in planar single-loop kinematic chains. It was found that in any planar single-loop chain formed by a set of links and revolute joints, the rotatability between any two links, whether they are adjoined or not, is independent of the order of connection. Simple and general approaches were also proposed to identify the exact rotatability between any two links of a single-loop N-bar chain. When a nonrevolvable link reaches the limit orientation with respect to another nonrevolvable link, disregard whether they are adjoined or not, all other links become collinear or parallel to each other. This paper fully extends Ting’s rotatability laws to deal with the rotatability between nonadjoined links.
Path Feasibility and Modification Based on the PUMA 560 Workspace Analysis
Authors: Shao Kuo-Chiang , Young Kuu-young
Published: June 2008

Robot paths are planned according to different industrial tasks. Their kinematic feasibility is restrained by the structure of the given robot manipulator. In order to design feasible paths under kinematic constraints and different task requirements, we propose first to utilize the geometry of the given robot to generate the geometric boundaries of different regions corresponding to kinematic constraints in the robot workspace. Geometric expressions are then derived to describe the relationship about the planned path and the robot workspace. Finally, by applying the developed modification strategies based on different task requirements, feasible paths can be obtained by modifying the infeasible portions of the paths. To demonstrate the proposed feasibility and modification schemes, the PUMA 560 robot manipulator is selected as a case study due to its complexity and practical application. The results are then extended to general wrist-partitioned types of industrial robot manipulators.
Structural Parameters Which Reduce the Number of Manipulator Configurations
Authors: Mavroidis C. , Roth B.
Published: June 2008

The inverse kinematics of series-chain, six-degree-of-freedom manipulators has been developed to the point where it yields all possible configurations for a given end-effector position and orientation. In this paper we use the methods of inverse kinematics to uncover the conditions on the structural parameters which cause a manipulator to yield a lower maximum number of configurations than its general class. It is shown that the following conditions can cause a diminution in the maximum number of possible configurations: parallel joint axes, perpendicular joint axes, intersecting joint axes, and Bennett geometries. Using these geometries in 6R, 5R1P, 4R2P, and 3R3P chains, this paper determines the reduction in degree of their characteristic polynomials.
Selective Backdriveability and Its Application to a Robotic Finger Design
Authors: Driels M. , Turkegenci Lt. Yavuz
Published: June 2008

The work reported covers the design of a prototype finger unit which will be part of a dexterous robotic hand design. Unlike conventional designs for contemporary hands which use tendons to actuate individual finger joints, this design uses small electric motors located in the finger units themselves. Because of high gear ratios in the final drive, the finger is able to sustain a grasp with power removed. An implementation of compliant joint control is discussed, and it is shown that this results in an actuation system which not only has variable stiffness control, but one in which the systems inability to be backdriven may be eliminated for those tasks where it is advantageous to do so.
Closed-Form Forward Displacement Analysis of the 4–5 In-Parallel Platforms
Authors: Lin Wei , Crane C. D. , Duffy J.
Published: June 2008

In this paper, we study a class of in-parallel platforms whose six legs are connected either singly or in a pair-wise fashion at the vertices of a quadrilateral top platform and a pentagonal base. A forward displacement analysis in closed-form is performed for each distinct case and polynomials ranging from 16th degree to 32nd degree are derived and verified numerically.
Forward Position Analysis of Nearly General Stewart Platforms
Authors: Zhang Chang-de , Song Shin-Min
Published: June 2008

This paper presents the closed-form solution of the forward position analysis of the nearly general Stewart platform, which consists of a base and a moving planar platform connected by six extensible limbs through spherical joints in the two planar platforms. It becomes a general Stewart platform if the centers are not constrained to those two planes. In this study, the coordinate transformation matrix is used to represent the position of the moving platform. Based on the six dependency equations of the rotation matrix and the six constraint equations related to the six link lengths, a set of six 4th degree equations in three unknowns are derived. Further derivations produce 21 dependent constraint equations. By simultaneous elimination of two unknowns a 20th order polynomial equation in one unknown is obtained. Due to dual solutions of other unknowns, this indicates a maximum of 40 possible solutions. The roots of this polynomial are then solved numerically and the realistic solutions are constructed using computer graphics.
Direct Position Analysis of the 4–6 Stewart Platforms
Authors: Chen Ning-Xin , Song Shin-Min
Published: June 2008

Although Stewart platforms have been applied in the design of aircraft and vehicle simulators and parallel robots for many years, the closed-form solution of direct (forward) position analysis of Stewart platforms has not been completely solved. Up to the present time, only the relatively simple Stewart platforms have been analyzed. Examples are the octahedral, the 3–6 and the 4–4 Stewart platforms, of which the forward position solutions were derived as an eighth or a twelfth degree polynomials with one variable in the form of square of a tan-half-angle. This paper further extends the direct position analysis to a more general case of the Stewart platform, the 4–6 Stewart platforms, in which two pairs of the upper joint centers of adjacent limbs are coincident. The result is a sixteenth degree polynomial in the square of a tan-half-angle, which indicates that a maximum of 32 configurations may be obtained. It is also shown that the previously derived solutions of the 3–6 and 4–4 Stewart platforms can be easily deduced from the sixteenth degree polynomial by setting some geometric parameters be equal to 1 or 0.
Dynamics Decomposition for Stewart Platforms
Authors: Ji Zhiming
Published: June 2008

This paper shows that special features of the Stewart platform can lead to the decomposition of the moving plate and the legs in the dynamic analysis. Formulas for evaluating, separately, the driving forces needed for the movement of the legs are developed for studying the combined inertia effect of all the leg rotations in a Stewart platform. The proposed formulation is easy to implement for Stewart platforms with nonnegligible leg inertia.
Dynamics of a Flexible Rod in a Quick Return Mechanism
Authors: Lee Heow-Pueh
Published: June 2008

The equations of motion in matrix form are formulated for a flexible rod in a quick return mechanism using Hamilton’s principle and the assumed mode method. The rod is considered as an Euler beam. The crank is assumed to be rigid and rotating at a constant angular speed. The translating-rotating joint connecting the crank to the flexible rod is assumed to be a frictionless moving point support for the flexible rod. This support is regarded as a very stiff spring acting on the rotating flexible rod. Results of numerical simulations are presented for various prescribed crank positions, crank lengths, and crank speeds.
Measurement of the Dynamic Model of a PUMA 560 Robot Using Experimental Modal Analysis
Authors: Elosegui P.
Published: June 2008

This paper presents two different models of the structural dynamics of a PUMA 560 robot: a frequency response, and a modal model. The first consists of a set of frequency response functions measured from the structure. The eigenvalues and the mode-shape, which comprise the modal model, are extracted from the response model. In addition to these linear models, the paper describes the nonlinear characteristics of the structure. How the non-linearities affect the measurement technique and the model accuracy is also described.
Toward a New Modeling Paradigm for Constrained Mechanical Systems
Authors: Hodges T. M. , Sheth P. N.
Published: June 2008

The motivational background and a comprehensive modeling framework for incorporating localized design details of joints in the overall multibody models are described in this paper. A direct contact model of two bodies in contact is utilized as a basic building block to develop spatial kinematic analysis procedures based on matrix analysis. A substructure partitioning method for large, detailed models and the concept of local Jacobians for localized joint models is introduced. The nonholonomic constraints are directly incorporated in the matrix method, with the special case of rolling without slipping described in this paper. The coordinate partitioning process is shown to play a fundamental role in the simulation algorithms. The developments reported in this paper represent initial steps toward a comprehensive modeling paradigm for multibody systems with a focus on the localized details of contacts between the bodies.
Solution Rectification in Three Position Motion Generation Synthesis
Authors: Waldron K. J.
Published: June 2008

In this paper the theory of solution rectification in motion generation synthesis of four-bar linkages is strengthened by presenting the mapping of the three-circle diagram into the center-point plane. This mapping may be used in conjunction with the corresponding mapping of the Filemon construction to eliminate solutions which must change branch to move through all of the design positions when cranks are generated by selecting their center-points. Earlier versions of the theory required that cranks be generated by selection of their circle-points.
Assemblability, Circuits, Branches, Locking Positions, and Rotatability of Input Links of Mechanisms With Four Closures
Authors: Kohli D. , Cheng Jyun-Cheng , Tsai K. Y.
Published: June 2008

A general analytical treatment is provided for determining conditions for assemblability, rotatability of input links, locking positions, and number of circuits of mechanisms with four closures and quartic input-output displacement polynomial. It is shown that assemblability, rotatability of input cranks, and lock positions are branch dependent properties for mechanisms with four closures and in general such mechanisms can have many branch dependent circuits. Such mechanisms may be assemblable for only two branches (instead of all four) and the input link rotatability is not only branch dependent but also starting position and direction of motion dependent. The input link may be continuously rotatable for one branch while for other branch it may go through one cycle of rotation (>2π but less than 4π) and then experience a locking position. A detailed analysis of assemblability, branching, locking positions, circuits, and rotatability is presented for spatial five-link RRRSR, RPRSR, RRPSR, and PRRSR mechanisms.
Grashof-Type Rotatability Criteria of Spherical Five-Bar Linkages
Authors: Kohli D. , Khonji A.
Published: June 2008

In this paper rotatability criteria of spherical five-bar linkages are analytically derived. First an equivalent linkage in which the sum of any two link lengths is less than π is found and then rotatability criteria of spherical five-bar linkages are developed for this linkage. The rotatability criteria developed in this paper are stated as follows: The two input angles are completely revolvable if and only if in the equivalent linkage the sum of the longest and the two shortest links is less than the sum of the remaining two links and there is one and only one long link between each pair of noninput angles (long link being any link excluding the shortest links). It is also shown that an angle θ included by two links αi and αj is completely revolvable if and only if the sum of the longest link and shorter of αi and αj is less than or equal to the sum of the remaining three links.
Development and Implementation of a Design for Producibility Method for Precision Planar Stamped Products
Authors: Schmitz J. M. , Desa S.
Published: June 2008

In this paper, we establish the Design for Producibility Design Development Methodology for stamped products which integrates both the design and manufacture of the stamped product. The general concept of considering manufacturing techniques at the initial design stages, often termed Design for Manufacturability, is certainly not novel. However, the proper implementation of this concept is not so widely understood. Our proposed method permits the product designer to control both product functionality (which he has incorporated into an initial design) and subsequent manufacturing costs through an iterative re-design process. The key step in this method is the mapping scheme from the final product design domain to the manufacturing domain; this scheme captures the cause-effect relations between design (and thus functional) specifications and manufacturing requirements and costs. We also describe the implementation of the design methodology in a knowledge-based computer environment called the Producibility Evaluation Package (P.E.P.) that, as a result of the design methodology, also automatically generates much of the process plan.
Spherical Maps: Their Construction, Properties, and Approximation
Authors: Gan J. G. , Woo T. C. , Tang K.
Published: June 2008

The Gaussian map and its allied visibility map on a unit sphere find wide applications for orientating the workpiece for machining by numerical control machines and for probing by coordinate measurement machines. They also provide useful aids in computerized scene analysis, computation of surface-surface intersection, component design for manufacturing and fabrication procedures. Spherical convex hulls and spherical circles are two geometric constructs used to approximate the Gaussian maps and the visibility maps. The duality and the complementarity of these spherical maps are examined so as to derive efficient algorithms.