bluuebunny/crossref_metadata_2025 huggingface dataset:
The Mobility Equation and the Solvability of Joint Forces/Torques in Dynamic Analysis
Authors: Song Shin-Min , Gao Xiaochun
Published: June 2008

The mobility equation has been applied to predict the indeterminacy of unknown joint forces/torques in static analysis. In this paper, the mobility equation is modified to investigate the solvability of joint forces/torques of spatial mechanisms in dynamic analysis. Each factor which may contribute to indeterminacy is discussed and is explicitly expressed in the equation. With the modifications, the mobility equation can be applied to a system with or without redundant actuators. Together with the concept of subspaces and a few simple rules, the mobility equation can be used to identify the solvability of every joint unknown, as well as the equations which are required for the solutions, under the assumption of rigid bodies. This method can be used as a guidance of dynamic analysis in dealing with complicated systems such as walking machines and multi-fingered grippers.
Closed-Form Solutions to the Spherical Joint Attachment Problem
Authors: Stanisˇic´ M. M. , Gupta K. C.
Published: June 2008

This paper presents closed-form solutions to the problem of defining the attachment of a spherical joint (a ball and socket) in a spatial linkage. The defined attachment should minimize the opening angle of the socket, maximizing the ball retention capability. Previous solutions to this problem have used iterative searching techniques, which are computationally intense. In this paper the problem is reformulated as a surface fitting problem. Two formulations are presented, both of which require the solution of the associated eigenvalue problems. The eigenvectors correspond to the central axis of symmetry for the socket opening. A numerical example is presented to compare the results obtained by these formulations with those available in the literature.
Determination of First and Second Order Instant Screw Parameters from Landmark Trajectories
Authors: Sommer H. J.
Published: June 2008

Least squares methods were developed to determine instant screw axis (ISA) and angular acceleration axis (AAA) parameters in experimental and analytical studies. The algorithms provide linear relationships for rigid body velocity and acceleration descriptors based on position, velocity, and acceleration data for individual points on the body. Weighted least squares estimators are presented for statistical weighting on individual landmarks as well as for variance weighting to reduce systematic measurement effects. The methods include instantaneous second order screw motion which describes differential geometry of screw axodes. Two spatial mechanism examples provide recommendations for landmark count, distribution, and placement.
Efficient Intersection of Surface Normals With Milling Tool Swept Volumes for Discrete Three-Axis NC Verification
Authors: Oliver J. H.
Published: June 2008

An efficient algorithm is presented for intersecting vectors with swept solids which represent three-axis numerically controlled (NC) milling tool motions. The intersection calculation proceeds in hierarchical steps through a series of progressively more exact definitions of the shape of the tool swept volume. At each step, results of intermediate calculations are used to determine whether intersection with an exact representation of the solid is possible and, if so, where and how the swept volume model must be refined for the next step. This structure ensures that superfluous intersection calculations are minimized. This intersection technique has been successfully implemented as part of an algorithm for automatic verification of three-axis NC milling programs, and may also be useful for applications in robotics and factory automation.
Computational Geometry on the Sphere With Application to Automated Machining
Authors: Chen Lin-Lin , Woo T. C.
Published: June 2008

Based on observations made on the geometry of the cutting tools and the degrees of freedom in 3-, 4-, 5-axis numerical control machines, a new class of geometric algorithms is induced on the unit sphere. Spherical algorithms are useful for determining the type of tool, its path, workpiece fixturing, and the type of machine. Basic to these algorithms are four that are presented here: detection of convexity on the sphere, computation for spherically convex hull, determination of the spherical convexity of a union, and the intersection of hemispheres. These four algorithms are related by duality and the sharing of partial results.
Implicit Numerical Integration of Constrained Equations of Motion Via Generalized Coordinate Partitioning
Authors: Haug E. J. , Yen Jeng
Published: June 2008

An implicit, stiffly stable numerical integration algorithm is developed and demonstrated for automated simulation of multibody dynamic systems. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. A stiffly stable, Backward Differentiation Formula (BDF) numerical integration algorithm is used to integrate independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, and accelerations, as well as Lagrange multipliers that account for constraints, are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The algorithm is shown to be valid and accurate, both theoretically and through solution of an example.
Design Sensitivity Analysis and Optimization of Nonlinear Structural Systems With Critical Loads
Authors: Park Jong Sang , Choi Kyung K.
Published: June 2008

A continuum formulation for design sensitivity analysis of critical loads is developed for nonlinear structural systems that are subjected to conservative loading. Both geometric and material nonlinear effects are considered. Sizing design variables such as cross-sectional areas of beam or truss design components and thicknesses of plate or membrane design components, together with their shape design variables, are treated. A continuum approach is used to obtain design sensitivity expressions in integral form. For shape design sensitivity analysis, the material derivative concept and domain method are used to find variations of the critical load due to variations in shape of the physical domain. The total Lagrangian formulation for incremental equilibrium equation and one-point linearized eigenvalue problems are utilized. A numerical method is presented to evaluate continuum design sensitivity expressions using analysis results of established finite element codes. It is found that no adjoint system is necessary for design sensitivity analysis of the critical load. Numerical results show the proposed method for design sensitivity of critical loads is accurate for both sizing and shape design variables. A numerical procedure for optimal design of nonlinear structural systems is presented, using the proposed continuum design sensitivity analysis method. An optimal design problem with a stability constraint is solved.
Computerized Simulation of Meshing and Bearing Contact for Single-Enveloping Worm-Gear Drives
Authors: Litvin F. L. , Kin V.
Published: June 2008

Single-enveloping worm-gear drives are considered. A general approach to computerized simulation of meshing for such misaligned drives is proposed. The proposed algorithm makes it possible to determine the transfer point where ideal line contact turns into real point contact and the transmission errors and the shift of bearing contact caused by the misalignment. Numerical examples for involute worm-gear drives are presented.
The Undercutting of Circular-Cut Spiral Bevel Gears
Authors: Fong Zhang-Hua , Tsay Chung-Biau
Published: June 2008

Undercutting is a serious problem in designing spiral bevel gears with small numbers of teeth. Conditions of undercutting for spiral bevel gears vary with the manufacturing methods. Based on the theory of gearing [1], the tooth geometry of the Gleason type circular-cut spiral bevel gear is mathematically modeled. The sufficient and necessary conditions for the existence and regularity of the generated gear tooth surfaces are investigated. The conditions of undercutting for a circular-cut spiral bevel gear are defined by the sufficient conditions of the regular gear tooth surface. The derived undercutting equations can be applicable for checking the undercutting conditions of spiral bevel gears manufactured by the Gleason Duplex Method, Helical Duplex Method, Fixed Setting Method, and Modified Roll Method. An example is included to illustrate the application of the proposed undercut checking equations.
A Design Methodology for System Parameters Synthesis of Elastic Planar Linkages: Theory
Authors: Boutaghou Zine-Eddine , Erdman A. G.
Published: June 2008

Existing formulations predict the displacement and stresses in multi-body systems that result from known system parameters. In contrast, the proposed design methodology enables structured selection of system parameters necessary to produce desired elastic displacements, stresses, and frequencies. This design process involves the development of inverse design equations, the finite element analysis, and the design sensitivity equations to obtain converged solutions satisfying desired design constraints. Part 1 (Theory) considers the theoretical considerations involved. Part 2 (Applications) applies the methodology to design a four-bar linkage and a six-bar linkage.
A Design Methodology for System Parameters Synthesis of Elastic Planar Linkages: Applications
Authors: Boutaghou Zine-Eddine , Erdman A. G.
Published: June 2008

The present paper describes the applicability of inverse design equations in conjunction with dynamic finite element analysis and design sensitivity features for multi-body dynamics. Whereas in Part 1 (Theory) of this paper we describe the general methodology with emphasis on an inverse design philosophy, Part 2 (Applications) presented here describes the integration of the total design process. Numerical examples are presented to validate the present developments for the design of multi-body systems.
A Synthesis Procedure for Design of 3-R Planar Robotic Workcells in Which Large Rotations Are Required at the Workpiece
Authors: Davidson J. K.
Published: June 2008

A new method is developed for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar 3-R robots that can provide dexterous workspace. The method is an adaptation of traditional techniques of linkage synthesis, and it is particularly well-suited to applications in which the motion-trajectory requires large rotations of the end-effector. It is determined that, when the trajectory requires that the end-effector rotate a full turn at just two locations and when the critical joint in the robot is rotatable by one turn, then the radial location of the workpiece is fixed in the workcell but its angular location is not fixed. When the mounting-angle of the tool is also a variable, the method accommodates trajectories in which the tool must rotate a full turn at three locations on the workpiece. The method can be applied not only to planar robots with three hinge-joints, but also to spatial robots, each with a planar 3-R module, when the principal attitudinal excursions of the trajectory are all about a set of parallel axes. Variables are identified, for both the motion-trajectory and the workpiece itself, which strongly affect the design of the workcell and the time for it to complete a motion-trajectory. Example problems illustrate the method. The new method is suggested as an alternative to the existing methods of computer science for motion-planning.
Autonomous Rectilinear Motion Planning for a Spatial Robot: Path Planning for a Spatial 4R Manipulator With a Single Spherical Obstacle Inside the Workspace
Authors: Shieh Menq-Dar , Duffy J.
Published: June 2008

This is the first of a series of papers dealing with the path planning for a spatial 4R robot with multiple spherical obstacles inside the workspace. In this paper, a time efficient algorithm has been developed to determine a collision free path for the end effector tip of the robot with a single spherical obstacle inside the workspace. A truncated pyramid and a right circular torus are used to model the nonreachable workspaces of the end effector tip of the robot. The problem of guiding the spatial 4R manipulator while avoiding a spherical obstacle is reduced to moving a point while avoiding a truncated pyramid and/or a right circular torus inside the workspace. The point represents the tip of the end effector of the manipulator. This approach produces an efficient algorithm for determining a collision free path. The algorithm has been successfully developed and implemented in the Silicon Graphics 4D-70GT workstation to verify the results.
Statics of In-Parallel Manipulator Systems
Authors: Agrawal S. K. , Roth B.
Published: June 2008

In-parallel systems can have some active and some passive joints (i.e., joints with and without joint actuators). The questions that we address in this paper are: how to choose the active and passive joints, how to know whether a set of active joints is sufficient, redundant, or minimal to control the end-effector, and whether there exists a unique choice of active actuators. Our approach to study this problem is based on instantaneous properties of series chains as derived from the theory of screw systems. In this framework, we identify those screws that correspond to the joint actuators of the component series chains. Once the correspondence is made, the sought after actuator properties are deduced from the vector space properties of these screws.
Least-Square Optimization of Planar and Spherical Four-Bar Function Generator Under Mobility Constraints
Authors: Liu Zheng , Angeles J.
Published: June 2008

An optimization scheme for four-bar function generators under mobility constraints, which can be applied to both planar and spherical four bar linkages, is presented in this paper. The design error, defined as the residual in the input-output equation, is minimized over the vector of linkage parameters. The mobility constraints, given as a set of inequalities, are converted into equalities by introducing slack variables. The problem is thus formulated as an equality-constrained minimization problem, which is then solved using the orthogonal-decomposition algorithm, an iterative numerical method introduced elsewhere. To reduce the dimensional unbalance, which often occurs in solving a synthesis problem, a penalty function is combined with the original objective function, whose minimization leads to dimensionally balanced linkages. A numerical example is included.
The Properties of Constant-Branch Four-Bar Linkages and Their Applications
Authors: Liu Zheng , Angeles J.
Published: June 2008

A four-bar linkage having a quadratic input-output equation can admit a constant value of the output variable for any value of the input variable. Such a linkage is termed constant-branch four-bar linkage in this paper. The general conditions governing the existence of this special class of linkages are derived through an in-depth analysis of the input-output equation. Geometric, mobility, and force-transmission properties are discussed with regard to most common types of planar, spherical, and spatial four-bar linkages. As an application example, a clutch mechanism, based on a constant-branch spatial RSSR four-bar linkage, is proposed.
A Geometric Approach to Hyper-Redundant Manipulator Obstacle Avoidance
Authors: Chirikjian G. S. , Burdick J. W.
Published: June 2008

The term hyper-redundant refers to redundant manipulators with a very large or infinite number of degrees of freedom. These manipulators are analogous in morphology to snakes, elephant trunks, and tentacles. While a variety of obstacle avoidance algorithms for nonredundant and mildly redundant manipulators exist, little analysis has been performed for hyper-redundant robots. This paper presents a strictly geometric algorithm for hyper-redundant manipulator obstacle avoidance which relies on the use of “tunnels” in the obstacle-filled workspace. Methods of differential geometry are used to formulate equations which guarantee that sections of the manipulator are confined to the tunnels, and therefore avoid obstacles. A general formulation is presented with an example to illustrate this approach.
Optimal Path Planning for Robot Manipulators
Authors: Muthuswamy S. , Manoochehri S.
Published: June 2008

The study reported in this paper deals with a computer-based methodology for the synthesis of an optimal tool path for robot manipulators in the presence of obstacles and singularities of the workspace. The methodology plans optimal path to achieve the best robot kinematic and dynamic performance criteria formulated through proper objective functions. The algorithm uses robot design parameters, the size and the location of the obstacles, and the initial and the goal states to generate a collision-free optimal tool path. Using these inputs the robot workspace is generated and discretized, and the obstacles are modeled as forbidden regions of the workspace. The search for the optimal path begins with the definition of a searchspace that includes the starting and the end points. All possible paths in the searchspace connecting these points are enumerated through the formation of a network graph structure. An intelligent heuristic search scheme has been developed to enumerate the network of allowable paths. The optimal path is then obtained as a sequence of via points connecting the initial and the final states by applying Dijkstra’s minimum cost algorithm. Contrary to most existing methodologies, the computational complexity of this algorithm decreases with an increase in the number and/or the size of the obstacles in the workspace. An interactive computer program has been developed to implement this methodology for a general planar two-link manipulator. This path planning methodology can be applied to any manipulator for which the workspace and the obstacles can be geometrically represented. The algorithm has been applied to some industrial SCARA robots and the results are discussed.
Functional Dependence and the Method of Alternate Formulations in Optimal Design
Authors: Hammond C. R. , Johnson G. E.
Published: June 2008

In an earlier article in this journal we introduced the Method of Alternate Formulations (MAF). MAF is a nonnumerical approach to constrained optimal design implemented with symbolic mathematics. The MAF problem formulation is the same as is used by the generalized reduced gradient method. There are usually many ways to partition the design vector into decision variable and state variable components and so there are usually many different alternate formulations for the objective function and constraints. Each alternate formulation contains all of the information about the physical system. Yet all other mathematical properties (e.g., convexity, linearity, scaling, etc.) can change. It has been observed that some of the alternate formulations that should exist based strictly on the theory of combinations cannot be obtained. In this paper, we show that this phenomenon occurs whenever there is functional dependence in the system model. Several examples are used to show how functional dependence affects the search for the solution by MAF. Prediction of functional dependence at the outset informs the designer which formulations cannot exist. This allows the designer to concentrate effort (more productively) on other formulations of the problem.
Automatic Finite Element Mesh Generation Over Domains Comprised of Multiply Connected, Intersecting, Rigid Body-Movable Subdomains
Authors: Yang Hyunik , Hoeltzel D. A.
Published: June 2008

An approach for the automatic generation and refinement of finite element meshes over nonconvex domains subdivided by multibody connected, rigid body-movable subdomains has been developed. The basis of this method relies in order on (1) the automatic insertion of nodes on the digitized boundaries and within the interiors of movable subdomains, (2) the generation of superelement meshes within the subdomains, (3) determination of intersection points between adjacent subdomains following their rigid body movement, (4) ensuring the satisfaction of interelement connectivity across subdomain boundaries, and (5) the interactive refinement of user-selectable subdomains using quadrilaterization for global refinement and triangularization for local refinement. The creation of a finite element mesh for an acetabular cup inserted in a human pelvis, which is representative of a mesh generated over complex, two-dimensional, multiply connected subdomains, as employed in an orthopedic total hip replacement, serves as a realistic application of this approach and demonstrates its utility for expeditiously performing finite element-based, parametric design studies.
Monotonicity Analysis of Taguchi’s Robust Circuit Design Problem
Authors: Wilde D. J.
Published: June 2008

Taguchi’s robust circuit design problem can be formulated rigorously as an optimization problem. A necessary condition for optimality is that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out to be monotonic in the remaining design variable, its optimum value must be at the limit of its range. The corresponding optimum value of the other variable is then determined exactly from the true, not approximate, constraint. Since no model construction, experimentation, statistical analysis, or numerical iteration is needed, this procedure is recommended whenever the input-output relation is known to be a monotonic algebraic function.
Multiobjective Design of Symmetrically Laminated Plates
Authors: Kumar N. , Tauchert T. R.
Published: June 2008

Multiobjective optimization of a symmetrically laminated composite plate is presented. Designs are obtained to realize maximum in-plane compressive load, maximum in-plane shear load, maximum bending strength, and maximum stiffness, two criteria being considered at a time. Design variables are fiber orientations and thicknesses of different layers. It is observed that nonconvex sets appear in the problem and consequently the weighting min-max method, rather than the pure weighting method, is used to reduce the vector maximum problem to a scalar one. Search for the optimum is then accomplished by a general nonlinear programming algorithm. Since exact solutions for the structural response are not available, the Rayleigh-Ritz method is employed to obtain approximate solutions. Numerical results are presented for different materials and various combinations of clamped, free and simply supported boundary conditions.
An Algorithm for Locating Feature Patterns for the Verification of Composite Positional Tolerancing
Authors: McCann M. J.
Published: June 2008

This paper develops an efficient software gage, suitable for real time inspection, to verify compliance with ANSI standard Y14.5 for composite positional tolerancing. The gage consists of a mathematical model and a computer algorithm. The model measures the maximum interference between a part and a feature pattern for any relative positioning of the feature pattern and part. The computer algorithm verifies compliance with the standard by precisely locating the feature pattern in rotation and translation for the minimum maximum interference. This is accomplished by first reducing minimum maximum interference suboptimized in translation to three generalized sets of lower bounds function in rotation and then searching the supremum of the lower bound functions over a unimodal interval of rotations for the global minimum.
An Approach for Concurrent and Integrated Material Selection and Dimensional Synthesis
Authors: Karandikar H. M. , Mistree F.
Published: June 2008

Difficulty in material selection is often mentioned as a reason for lengthy design cycles. Problems dealing with material selection play a central role in almost all design and are generally tackled using the experience-based judgment of a designer. Better methods for material selection are needed, however, because demands of efficient operation require judicious use of materials and there is increasing pressure to reduce costs. To date, material selection and dimensional synthesis of artifacts have mostly been tackled sequentially rather than concurrently. In this paper, a domain-independent, algorithmic method to guide a designer in the material selection phase of design is presented. The method enables concurrent determination of the material and the dimensions for an artifact. The approach, applicable to any material selection and design problem, is illustrated by a case study dealing with the design of a component made of composite materials.
Design and Geometry of Face-Gear Drives
Authors: Litvin F. L. , Zhang Y. , Wang J.-C. , Bossler R. B. , Chen Y.-J. D.
Published: June 2008

The authors have developed the analytical geometry of face-gear drives, proposed the method for localization of bearing contact, developed computerized simulation of meshing and bearing contact, investigated the influence of gear misalignment on the shift of bearing contact and transmission errors. Application for design is discussed. The obtained results are illustrated with numerical examples.
A Formal Approach to Specifications in Conceptual Design
Authors: Kusiak A. , Szczerbicki E.
Published: June 2008

In this paper, a methodology for the specification stage in conceptual design is presented. The specification stage provides requirements and transforms them into functions of the designed object. It occurs at the highest level of abstraction and it must provide enough information for the synthesis process where functions are transformed into design components that are further synthesized into the designed object. The proposed approach includes the following issues: specification of requirements, specification of functions, incorporation of logic into functional and requirement trees, representation of requirements-functions interaction, and optimization in the functional space. The methodology presented is illustrated with examples. Key words: design requirements, design specifications, conceptual design, design process, artificial intelligence, formal method
Design Formulae for Elliptical Cross-Section Helical Springs
Authors: Nagaya Kosuke , Hirata Yasuo , Tsurumi Toyoaki , Takeda Sadahiko , Nagai Ken-ichi , Tanifuji Katsuya
Published: June 2008

The maximum stress in elliptical cross-section coil springs with a certain aspect ratio becomes small as compared to the other springs used in practical machines. This article presents a simplified stress expression for designing elliptical cross-section coil springs. The stresses obtained by the present design formula are compared with those by calculated using numerical methods. It is ascertained that the present formula is applicable to design the elliptical cross-section coil springs.
Formulation of a Mechanical Model for Composites With Embedded SMA Actuators
Authors: Jia J. , Rogers C. A.
Published: June 2008

Shape memory alloy reinforced composites are an extremely versatile class of materials with adaptive characteristics that may be exploited for damage control, active structural acoustic control, dynamic tuning, and shape control. In order to design structures reliably with embedded shape memory alloy actuators, a fundamental mechanical model must be formulated to predict the materials’ variable stiffness, induced moments and loads, and the change of curvature that can result. The mechanical model described in this paper is formulated from the micromechanical behavior of the highly nonlinear shape memory alloy actuators and classical lamination theory. The behavior of typical shape memory alloys will be presented and then used in formulating a one- and two-dimensional model and the results will be applied to plate theory.
Dimensional Synthesis of Closed-Loop Linkages to Match Force and Position Specifications
Authors: Huang C. , Roth B.
Published: June 2008

By combining classical kinematic synthesis and static synthesis, we consider force conditions as well as motions in the dimensional synthesis of linkages. We are concerned with determining the dimensions of linkages that guide a rigid body through several positions and support a specified external load at each position. Three types of planar linkages are studied in detail: four-bar, slider-crank, and double-slider linkages. Incompletely specified problems and spring element synthesis are also discussed.
Design of Multi-Degree-of-Freedom Mechanisms for Optimal Dynamic Performance
Authors: Shiller Z. , Sundar S.
Published: June 2008

Design methods for selecting the actuator sizes and the link lengths of multi-degree-of-freedom mechanisms for minimum time motions along specified paths and between given end points are presented. The design problem is first formulated as a parameter optimization, using the actuator sizes and the link lengths as the design variables, and motion time along the path as the cost function. A more efficient method for obtaining near-optimal designs is then presented, based on the acceleration lines which have been shown to approximate the geometric shapes of time optimal paths [15]. Near-optimal designs are simply obtained by curve-fitting the acceleration lines to the desired path, or to the end points. Examples of the design of two and five-bar mechanisms demonstrate significant reductions in motion times for the optimal and the near-optimal designs, and significant savings in computation time for the approximate method.
Kinematic Modules for Singularity-Free Movement With Three Cartesian Freedoms
Authors: Long G. L. , McCarthy J. M. , Paul R. P.
Published: June 2008

The singularity conditions of three-revolute-joint serial chain manipulators are investigated by considering the motion of an arbitrary point on a terminal link. A distinction is made between singular configurations (every point on the terminal link is singular) and singular surfaces (a chosen point on the terminal link lies on a singular surface). Of particular interest is a class of 3R manipulators—each manipulator within this class forms a third-order screw system. We outline the structural requirements for this 3R class, and then determine the singularity conditions for several cases. For several manipulators within this 3R class, we describe a strategy to develop four-revolute-joint kinematic modules for singularity-free movement with three Cartesian freedoms. The algorithm to control the kinematic modules is simple and can be implemented in real-time.
Circuit Analysis of Watt Chain Six-Bar Mechanisms
Authors: Mirth J. A. , Chase T. R.
Published: June 2008

A circuit is a distinct continuous range of motion of a mechanism. Changing circuits necessitates disassembling the mechanism. Thus, a designer must ensure a mechanism does not change circuits between two desired positions. A Watt chain is composed of two connected four-bar chains. A Watt chain may have one, two, three, or four circuits. The number of circuits and the extent of each circuit are shown to be determinable from the circuit attributes of the two component four-bars and by the limits of motion that these two four-bars place on each other. The circuit composition of all pin jointed Watt mechanisms is summarized in chart form. The chart enables detecting a change of circuit between any two trial positions of the same mechanism. The chart is suitable for both automated and manual analysis. Examples of circuit analysis of both Watt I and Watt II mechanisms are provided.
Determining the Effects of Coulomb Friction on the Dynamics of Bearings and Transmissions in Robot Mechanisms
Authors: Gogoussis A. , Donath M.
Published: June 2008

In order to accurately model robots for precision applications where dynamics are significant, it is important to include the effects of Coulomb friction in the bearings and transmissions. The general guidelines for analyzing friction at the joints will be discussed. It will be shown that friction can be related to the joint coordinates and their first and second time derivatives. The resulting extended robot dynamics formulation will be investigated as it applies to the inverse and forward robot dynamics problems. The analytical dependency of Coulomb friction on joint interactions is explicitly examined. As an illustration of friction effects in transmissions, we elaborate on the friction in harmonic drives and develop a method for its evaluation. The effect of friction in the bearings on the dynamics is also considered and a quantitative characterization of several specific cases is provided. This study is significant to understanding the design and control issues as they relate to achieving high speed precision robot motion.
Kinematic and Dynamic Synthesis of Geared Robotic Mechanisms
Authors: Chen Dar-Zen , Tsai Lung-Wen
Published: June 2008

This paper describes a methodology for the design of geared robotic mechanisms. It is shown that certain gear-coupled manipulators can be designed to possess kinematic isotropy property at a given end-effector position. For these gear-coupled manipulators, the train values can be treated as a product of two-stage gear reductions. The second-stage reduction can be uniquely determined from the kinematic isotropic conditions, while the first-stage reduction can be determined from dynamic considerations. This approach, through proper choice of gear ratios, can provide these gear-coupled manipulators with desired kinematic and dynamic characteristics.
On the Redundant-Drive Backlash-Free Robotic Mechanisms
Authors: Chang Sun-Lai , Tsai Lung-Wen
Published: June 2008

In this paper, we introduce a new and innovative concept for the control of backlash in gear-coupled robotic mechanisms. The concept utilizes redundant unidirectional drives to assure positive coupling of gear meshes at all times. Based on this concept, a methodology for the enumeration of admissible redundant-drive backlash-free robotic mechanisms has been established. Some typical two- and three-DOF mechanisms have been sketched. Furthermore, actuator torques have been derived as functions of either joint torques or end-effector dynamic performance requirements. A redundantly driven manipulator has the fail-safe advantage in that, except for the loss of backlash control, it can continue to function when one of its actuators fails. It does not have the compliance problem associated with tendon-driven manipulators. A two-DOF backlash-free experimental arm is currently under construction to demonstrate the principle.
On the Necessary and Sufficient Conditions for Homokinetic Transmission in Chains of Cardan Joints
Authors: Johnson D. A. , Willems P. Y.
Published: June 2008

The classical double universal joint for constant velocity ratio transmission is subject to strict geometrical requirements as regards configuration, and it is generally accepted that similar constraints also prevail for longer chains of joints. This paper examines the constant velocity conditions from a necessary point of view and establishes new configuration possibilities for chains of 3 or more joints, which allow to envisage more flexible design in some applications.
Five Position Triad Synthesis With Applications to Four- and Six-Bar Mechanisms
Authors: Subbian T. , Flugrad D. R.
Published: June 2008

The displacement equations for trials with motion generation and prescribed timing capabilities are developed and cast in polynomial forms. These equations are solved for five precision points using a continuation method. A detailed description of the method used to generate the solution curves is provided in the paper. Two infinities of solutions can be obtained for the problem under consideration as we are solving four equations in six unknowns. The solution procedure discussed is applied to synthesize a four-bar function generating mechanisms and a six-bar mechanism.
The Workspace of a General Geometry Planar Three-Degree-of-Freedom Platform-Type Manipulator
Authors: Pennock G. R. , Kassner D. J.
Published: June 2008

This paper focuses on the direct workspace problems of a general geometry fully-parallel-actuated, planar three-degree-of-freedom platform-type manipulator. A set of equations are presented that determine the workspace as a function of the platform orientation. The formulation is governed by the solution to the inverse position problem of the manipulator. The reachable positions of the end-effector point, for a specified platform orientation, are analyzed. To illustrate the concepts, a practical example is included where the end-effector is required to move a cup filled with water. Then the platform orientation, for a specified location of the end-effector point, is studied. If an arbitrary orientation is possible, the specified location of the end-effector point is said to be within the primary workspace. The paper includes a detailed discussion of the total primary workspaces of the manipulator. The approach adopted here is to regard the manipulator as a combination of three planar, three-revolute open chains. For the sake of completeness, the influence of special manipulator geometry on the workspace is also discussed. Finally, the paper includes the conditions that cause stationary configurations of the manipulator. Insight into these undesirable configurations is provided by a study of the location of the absolute instant center of the platform.
Mapping of Kinematic and Dynamic Parameters for Coupled Manipulators
Authors: Ji Zhiming , Leu Ming C.
Published: June 2008

Industrial manipulators use various types of transmissions, such as gears, belts, chains, and parallel mechanisms, to transmit driving power to the links. By arrangement many such transmissions cause coupled joint motions. Manipulators having coupled joint motions are referred to as coupled manipulators. Conventional methods for constructing Jacobian matrix and compliance matrix are not directly applicable to coupled manipulators. The concept of the mapping matrix is used in this paper for establishing relationships of torque, speed, Jacobian and compliance of these manipulators with those obtained with conventional methods. A method of constructing the mapping matrix systematically is discussed. Two examples show that the proposed method is easy to implement.
Inverse Dynamics of a Flexible Robot Arm by Optimal Control
Authors: Kokkinis T. , Sahraian M.
Published: June 2008

The problem of end-point positioning of flexible arms is discussed. Because of the nonminimum phase nature of the problem, inversion fails to produce bounded joint torques. Bounded noncausal joint torques for achieving the task of end-point tracking for a multilink arm are found using optimal control theory. The torques obtained have no high-frequency content, and are suitable for practical applications. The method is illustrated by simulation of a single-link arm, for which stability and robustness considerations for design are given.
Flexible Multibody Dynamics Based on a Fully Cartesian System of Support Coordinates
Authors: Vukasovic N. , Celigu¨eta J. T. , Garci´a de Jalo´n J. , Bayo E.
Published: June 2008

In this paper we present an extension to flexible multibody systems of a system of fully cartesian coordinates previously used in rigid multibody dynamics. This method is fully compatible with the previous one, keeping most of its advantages in kinematics and dynamics. The deformation in each deformable body is expressed as a linear combination of Ritz vectors with respect to a local frame whose motion is defined by a series of points and vectors that move according to the rigid body motion. Joint constraint equations are formulated through the points and vectors that define each link. These are chosen so that a minimum use of local reference frames is done. The resulting equations of motion are integrated using the trapezoidal rule combined with fixed point iteration. An illustrative example that corresponds to a satellite deployment is presented.
The Geometry of Interference With Application to Obstacle Avoidance
Authors: Choi Y. J. , Crane C. D. , Matthew G. K. , Duffy J.
Published: June 2008

A mapping which transforms the relative displacements of one object with respect to a reference object into image points has been developed by interpreting the relative displacement in terms of affine coordinates. The mapping provides a novel mathematical tool that solves interference problems of objects in three-dimensional space. By use of this mapping, the geometrical condition of interference of objects is represented by simple inequalities. The inverse mapping provides the means of avoiding interference and can be utilized for articulation of robot arms so as to avoid collision with obstacles.
Optimum Tolerancing of Planar Mechanisms Based on an Error Sensitivity Analysis
Authors: Cleghorn W. L. , Fenton R. G. , Fu Jing-fan
Published: June 2008

This paper presents an analytical procedure to determine the optimum set of tolerance bands of the dimensions of a planar mechanism. Optimum tolerance bands are those which allow the largest values of dimensional tolerances, while ensuring that the desired output motion is kept within acceptable deviations form the output that would be generated by an ideal mechanism having no errors in dimensions. The analysis technique presented permits identification of the most sensitive link dimension, the most sensitive combination of input errors, and the most sensitive period within the entire cycle, which make the largest contribution to the output error. The optimum tolerancing procedure is then presented. Examples applied to single and multiple loop mechanisms are included.
An Analytical Method for the Identification of Redundant Constraints in Multiple-Loop Spatial Mechanisms
Authors: Srivatsan R. , Hoeltzel D. A. , Das A.
Published: June 2008

An analytical method for the explicit identification of redundant constraints in multiple-loop spatial mechanisms is presented. The kinematic constraint equations for each independent loop of multiple-loop mechanisms are developed. The independence of these equations is established and used to detect the presence of redundant constraints. The nature of the redundant constraints present is indicated by the type of redundant kinematic constraint equations present. Interaction of the constraints of adjacent loops in a multiple-loop mechanism also has to be taken into account. An example which illustrates the identification of redundant constraints in a cardan joint has been included to demonstrate the utility of this approach for real-world mechanism design problems. General guidelines for the elimination of redundant constraints, following their identification, are also provided.
The Opposite Pole Quadrilateral as a Compatibility Linkage for Parameterizing the Center Point Curve
Authors: McCarthy J. M.
Published: June 2008

In planar four-position kinematics, the centers of circles containing four positions of a point in a moving rigid body form the center point curve. This curve can be parameterized by analyzing a “compatibility linkage” obtained from a complex number formulation of the four-position problem. In this paper, we present another derivation of the center point curve using a special form of dual quaternions and the fact that it is identical to the pole curve. The defining properties of the pole curve lead to a parameterization by kinematic analysis of the opposite pole quadrilateral as a four-bar linkage. Thus the opposite pole quadrilateral becomes the compatibility linkage. This derivation generalizes to provide parameterizations for the center point cone of spherical kinematics and the central axis congruence of spatial kinematic theory.
The Performance of a Mechanical Design ‘Compiler’
Authors: Ward A. C. , Seering W. P.
Published: June 2008

A mechanical design “compiler” has been developed which, given an appropriate schematic, specifications, and utility function for a mechanical design, returns catalog numbers for an optimal implementation. The compiler has been successfully tested on a variety of mechanical and hydraulic power transmission designs, and a few temperature sensing designs. Times required have been at worst proportional to the logarithm of the number of possible combinations of catalog numbers.
Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections
Authors: Bagci C.
Published: June 2008

Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.
Compatibility-Based Design for Contact Stress
Authors: Ishii K. , Klinger J. M. , Hamrock B. J.
Published: June 2008

This paper discusses the combined use of quantitative analysis equations and knowledge-based techniques in the design of machine elements. We introduce the method of design compatibility analysis to (1) guide the application of correct analysis equations, (2) interpret the results of analysis, and (3) suggest modifications to improve the design. As an example vehicle, this paper focuses on design issues related to contact stresses and lubrication between two surfaces. The compatibility approach covers not only quantitative performance measures, but also the qualitative design issues such as suitability of surface materials, machining methods, surface roughness, lubricants, etc. To verify the utility of this concept, we developed DECS (Design Expert for Contact Stress), a PC-based design-aid for contact stresses and lubrication. DECS uses Prolog for top-level management and inference, while C provides the efficient computation of the quantitative equations. DECS also utilizes some recent developments in the computations of contact stress and elastohydrodynamic lubrication. Our method would be useful in many other design applications.
On Optimum Truss Layout by a Homogenization Method
Authors: Di´az A. R. , Belding B.
Published: June 2008

A new approach to the truss layout optimization problem is possible by using homogenization theory. Unlike traditional methods for optimization of truss topology, the new method does not require that the set of admissible connecting points be defined a-priori. This represents a great advantage over other strategies, which may inadvertently exclude optimum solutions by prescribing a set of connecting points that is inconsistent with the optimum connectivity. The homogenization approach, however, is based on the solution of the equations of plane elasticity over a two dimensional domain and its solutions are only truss-like structures. The relationship between these solutions and optimum truss structures is examined.