bluuebunny/crossref_metadata_2025 huggingface dataset:
Logical Foundations of Kinematic Chains: Graphs, Line Graphs, and Hypergraphs
Authors: Harary Frank , Yan Hong-Sen
Published: June 2008

In terms of concepts from the theory of graphs and hypergraphs we formulate a precise structural characterization of a kinematic chain. To do this, we require the operations of line graph, intersection graph, and hypergraph duality. Using these we develop simple algorithms for constructing the unique graph G (KC) of a kinematic chain KC and (given an admissible graph G) for forming the unique kinematic chain whose graph is G. This one-to-one correspondence between kinematic chains and a class of graphs enables the mathematical and logical power, precision, concepts, and theorems of graph theory to be applied to gain new insights into the structure of kinematic chains.
Generalized Solution for the Optimal Prehension State Using End Effectors With Multi-Articulated Fingers
Authors: Badreldin A. , Seireg A.
Published: June 2008

A general formulation for the mechanics of the grasp with elastic multi-articulated fingers is presented. A procedure utilizing linear programming is given for computing a unique solution for the normal forces as well as the frictional forces and moments at the contact areas which insures stability of the grasp at the considered configuration. The procedure is particularly useful when the deformation or precision movement of the grasped object is of importance. An efficient optimization algorithm is also given to determine the best grasping configuration for any shape object undergoing any task using end effectors with any number of fingers.
Matrix Analysis Method for Direct and Multiple Contact Multibody Systems
Authors: Sheth P. N. , Hodges T. M. , Uicker J. J.
Published: June 2008

A generalized modeling procedure for curves and surfaces in direct contact relative motions is developed, such that these joints can be consistently included in the well-developed and established (4 × 4) matrix method for kinematic, static, and dynamic analyses of geometrically constrained lower paired multibody mechanical systems. The modeling procedure allows both the analytical and the discretized Geometric Modeling approaches. As one application of these analytical techniques, a numerical procedure for mobility analysis of multiple contact joints is presented and illustrated. Other applications of this development are enumerated.
Spatial Dynamics of Deformable Multibody Systems With Variable Kinematic Structure: Part 2—Velocity Transformation
Authors: Chang C. W. , Shabana A. A.
Published: June 2008

In Part 1 of these two companion papers, the spatial system kinematic and dynamic equations are developed using the Cartesian and elastic coordinates in order to maintain the generality of the formulation. This allows introducing general forcing functions and adding and/or deleting kinematic constraints. In control applications, however, it is desirable to determine the joint forces associated with the joint variables. On the other hand the use of the joint coordinates to formulate the dynamic equations leads to a complex recursive formulation based on loop closure equations. In this paper a velocity transformation technique applicable to spatial multibody systems that consist of interconnected rigid and deformable bodies is developed. The Cartesian variables are expressed in terms of the joint and elastic variables. The resulting kinematic relationships are then employed to determine the joint forces associated with the joint variables. A spatial robot manipulator that manipulates an object is presented as a numerical example to exemplify the development presented in this paper.
Determination of Bearing Reactions of Spatial Linkages and Manipulators
Authors: Litvin F. L. , Tan J.
Published: June 2008

Application of D’Alembert’s principle for determination of dynamic bearing reactions in joints of spatial linkages and parallel manipulators needs the simultaneous solution of a large system of equations. The authors of this paper propose an approach that is a combined application of principle of virtual work and D’Alembert’s principle. The main advantages of the proposed approach are: (1) reduction of the number of equations that have to be solved simultaneously, and (2) simplification of the expressions for the relative virtual velocity. The proposed approach is illustrated with the example of a 7-bar linkage and its application is explained with the crank-slider linkage.
Large-Displacement Finite Element Analysis of Flexible Linkages
Authors: Yang Zhijia , Sadler J. P.
Published: June 2008

A finite element model is derived for flexible planar linkages, treating the total mechanism displacements as the primary unknowns in the dynamic equations of motion. These displacements consist of the combination of large rigid-body mechanism motion and small elastic deformations. Beam elements are used in the model formulation. The resulting nonlinear equations can be solved under conditions of either specified input motion of the mechanism or specified input forcing functions. In either case, the differential equations are integrated numerically. Illustrative examples are presented, and comparisons are made with results of previous investigators and with results from a commercial finite element code.
A Theoretical and Experimental Investigation of the Dynamic Response of a Slider-Crank Mechanism With Radial Clearance in the Gudgeon-Pin Joint
Authors: Soong K. , Thompson B. S.
Published: June 2008

A comprehensive analytical investigation of the dynamic response of a general planar kinematic chain comprising an assemblage of articulating interconnected rigid-bodies with bearing clearances in the revolute joints is presented. The equations governing the dynamical behavior of this general mechanical system are established by incorporating a four-mode model of the phenomenological behavior of the principal elements of each revolute joint into the generalized form of Lagrange’s equations. The proposed methodology is then employed to predict the dynamic behavior of a planar slider-crank mechanism with radial clearance in the gudgeon-pin joint prior to comparing these theoretical predictions with the corresponding response-data from a complementary experimental investigation.
Pattern Matching Synthesis as an Automated Approach to Mechanism Design
Authors: Hoeltzel D. A. , Chieng Wei-Hua
Published: June 2008

A new knowledge-based approach for the synthesis of mechanisms, referred to as Pattern Matching Synthesis, has been developed based on a combination of committee machine and Hopfield neutral network models of pattern classification and matching applied to coupler curves. Computational tests performed on a dimensionally-parameterized four bar mechanism have yielded 15 distinct coupler curve groups (patterns) from a total of 356 generated coupler curves. This innovative approach represents a first step toward the automation of mapping structure-to-function in mechanism design based on the application of artificial intelligence programing techniques. Demonstrative examples of its application to “real-world” mechanism synthesis problems, including the design and evaluation of a two-stroke pump mechanism and the redesign of a variable-stroke engine mechanism have been included, establishing its viability for creative mechanism synthesis.
Analysis and Optimal Design of Spatial Mechanical Systems
Authors: Ashrafiuon H. , Mani N. K.
Published: June 2008

This paper presents a new approach to optimal design of large multibody spatial mechanical systems which takes advantage of both numerical analysis and symbolic computing. Identification of system topology is carried out using graph theory. The equations of motion are formulated in terms of relative joint coordinates through the use of a velocity transformation matrix. Design sensitivity analysis is carried out using the direct differentiation method applied to the relative joint coordinate formulation for spatial systems. The symbolic manipulation program MACSYMA is used to automatically generate the necessary equations for both dynamic and design sensitivity analyses for any spatial system. The symbolic equations are written as FORTRAN statements that are linked to a general purpose computer program which performs dynamic analysis, design sensitivity analysis, and optimization, using numerical techniques. Examples are presented to demonstrate reliability and efficiency of this approach.
Building an Expert System for Engineering Design Based on the Object-Oriented Knowledge Representation Concept
Authors: Akagi S. , Fujita K.
Published: June 2008

An expert system is developed for engineering design based on an object-oriented knowledge representation concept. The design process is understood as determining design variables and their relationships which compose the design model. The design model is represented as a network in the computer system using the object-oriented knowledge representation. The system built with the above concept provides the following abilities: (1) flexible model building and easy modification, (2) effective diagnosis of the design process, (3) supporting method for redesign, (4) a hybrid function with numerical computations and graphics, and (5) applicability for various design problems. Finally, it is applied to the basic design of a ship.
Nonlinear Integer and Discrete Programming in Mechanical Design Optimization
Authors: Sandgren E.
Published: June 2008

A general purpose algorithm for the solution of nonlinear mathematical programming problems containing integer, discrete, zero-one, and continuous design variables is described. The algorithm implements a branch and bound procedure in conjunction with either an exterior penalty function or a quadratic programming method. Variable bounds are handled independently from the design constraints which removes the necessity to reformulate the problem at each branching node. Examples are presented to demonstrate the utility of the algorithm for solving design problems.
Limitations of Conjugate Gear Tooth Surfaces
Authors: Litvin F. L. , Kin V. , Zhang Y.
Published: June 2008

Gear tooth surfaces being in line contact at every instant are considered. The dimensions of the contacting surfaces must be limited in order to avoid: (a) the appearance of the envelope of lines of contact on the generating surface Σ1, and (b) the appearance of singular points on the generated surface Σ2. The relations between the developed concepts and Wildhaber’s concept of the limiting pressure angle are investigated. Applications to the worm-gear drive and the generation of a pinion of a Formate gear drive are considered. Computer graphics have been used to illustrate the results of computation.
An Analytical Study of Automotive Neutral Gear Rattle
Authors: Comparin R. J. , Singh R.
Published: June 2008

A reduced order nonlinear model of an automotive manual transmission is presented and the neutral rattle case is analyzed. For a single frequency excitation and primary resonance, approximate analytical solutions are developed for a multi-degree-of-freedom model of a transmission using the method of harmonic balance. Based on these solutions, a simplified set of equations is developed for the study of neutral gear rattle and the use of these equations for design studies is illustrated. The nonlinear frequency response characteristics are discussed and the results are compared to similar studies described in the literature. It is shown that this analysis provides an improved understanding of the neutral gear rattle problem as well as an analytical basis for the nonlinear behavior reported in the literature.
Investigation of Weibull Statistics in Fracture Analysis of Cast Aluminum
Authors: Holland F. A. , Zaretsky E. V.
Published: June 2008

The fracture strengths of two large batches of A357-T6 cast aluminum coupon specimens were compared by using two-parameter Weibull analysis. The minimum number of these specimens necessary to find the fracture strength of the material was determined. The applicability of three-parameter Weibull analysis was also investigated. A design methodology based on the combination of elementary stress analysis and Weibull statistical analysis is advanced and applied to the design of a spherical pressure vessel shell. The results from this design methodology are compared with results from the applicable ASME pressure vessel code.
A Study of the Dynamics of a Split-Torque, Geared-Neutral Transmission Mechanism
Authors: Hanachi S.
Published: June 2008

A Split-Torque, Geared-Neutral mechanism offers considerable potential as a continuously variable transmission. However, dynamics, control, and driveability issues associated with power recirculation, performance during launch, and mode shift, can only be resolved with the help of a predictive mathematical model. A model, which allows for all anticipated changes in the kinematic structure, has been developed. A separate analysis is performed for each kinematic structure, with the frictional losses being characterized by external torques. The transmission is considered to be a part of a complete powertrain so that the simulation results can be evaluated in terms of vehicle performance criteria. Simulation results indicate correct qualitative behavior, and are included to illustrate the use of the model. Furthermore, these results provide insight into functional relationships existing between input commands and system performance, a prerequisite to developing control laws.
Experimental Study on the Elastodynamic Behavior of the Unbalanced and the Counterweighted Four Bar Mechanisms
Authors: Raghu E. , Balasubramonian A.
Published: June 2008

In one of the earlier papers reported in two parts, the authors have presented the theory and the experimental results concerning the elastodynamic behavior of an endweighted elastic coupler of a four bar mechanism. The aim of this paper is to present some detail regarding the experimental setup for measuring the shaking force and briefly regarding the measurement of the elastic coupler response of a four bar mechanism. However, it is believed that this kind of design principle can also be used in other applications.
The End-Effector Angle and Manipulator Dexterous Workspaces
Authors: Song Shin-Min , Lei Chi Meng , Wang Jiang
Published: June 2008

The end-effector angle is defined as the angle between the end-effector axial axis and the hand axis (an axis from the wrist center to the end-effector reference point). Most industrial manipulators posses a zero end-effector angle. This paper shows that the dexterity of a manipulator, which is indexed by the volume of dexterous workspace, is affected by the end-effector angle. Three 6-d.o.f., anthropomorphic manipulators and three types of dexterous workspace are used to study this influence. The results show that, for all three manipulators, the volume of a dexterous workspace in general increases along with the end-effector angle and it reaches maximum value when the end-effector angle is 90 deg. This influence is very obvious with the reachably dexterous workspace and the 180 deg spinnably dexterous workspace and is less obvious with the 360 deg spinnably dexterous workspace. These results somewhat confirm the fact that the majority of human hand prehensions used in daily life operations apply a nonzero end-effector angle.
Mechanical Design of Variable Configuration Tracked Vehicle
Authors: Iwamoto Taro , Yamamoto Hiroshi
Published: June 2008

A terrain-adaptable tracked vehicle suitable for traveling over a variety of surfaces, including stairways, with features of low energy consumption, high speed, and light weight, has been designed and developed. Active terrain adaptability is performed by the variable track configuration scheme, which can be changed to suit temporary road conditions. Many requirements for the robot vehicle, such as simple track configuration control, suspension for high road grip, reduction of turning resistance force, coexistence of high climbing ability and high speed on flat surfaces, and reduced tare weight, have been achieved mechanically without disturbing variable track configuration characteristics.
Sensitivity Analysis of the Burmester Equations of Planar Motion
Authors: Mahableshwarkar S. V. , Kramer S. N.
Published: June 2008

In this paper the sensitivity of the configuration of a mechanism to small variations in the precision point locations and corresponding coupler rotations is presented. The changes in the locations of the centerpoints and circlepoints, hence the dyads constituting the mechanism, due to these variations are determined by evaluating the total differentials of these quantities. The method is applied to mechanisms designed by the Burmester Theory of Planar Motion for four precision and five precision points. This additional information on sensitivity is shown to be useful in the iterative process of mechanism design. Numerical examples and an applications section are included to illustrate the formulation and show how this concept can be applied to mechanism design.
Dynamic Modeling and Simulation of Flexible Robots With Prismatic Joints
Authors: Pan Ye-Chen , Scott R. A. , Ulsoy A. Galip
Published: June 2008

A dynamic model for flexible manipulators with prismatic joints is presented in Part I of this study. Floating frames following a nominal rigid body motion are introduced to describe the kinematics of the flexible links. A Lagrangian approach is used in deriving the equations of motion. The work done by the rigid body axial force through the axial shortening of the link due to transverse deformations is included in the Lagrangian function. Kinematic constraint equations are used to describe the compatibility conditions associated with revolute joints and prismatic joints, and incorporated into the equations of motion by Lagrange multipliers. The small displacements due to the flexibility of the links are then discretized by a displacement based finite element method. Equations of motion are derived for the cases of prescribed rigid body motion as well as prescribed joint torques/forces through application of Lagrange’s equations. The equations of motion and the constraint equations result in a set of differential algebraic equations. A numerical procedure combining a constraint stabilization method and a Newmark direct integration scheme is then applied to obtain the system response. An example, previously treated in the literature, is presented to validate the modeling and solution methods used in this study.
Synthesis of a Controllable Circuit Breaker Mechanism
Authors: Jobes C. C. , Palmer G. M. , Means K. H.
Published: June 2008

This paper addresses, for the first time, the synthesis, optimization, simulation and analysis of a controllable circuit breaker mechanism. Type synthesis is performed by finding the mechanisms conforming to topological requirements set forth in the problem definition and evaluating them to determine whether they satisfy the stated functional requirements. Dimensional synthesis is performed upon these mechanisms by designating the equality and inequality constraints, assigning the variable types, and then searching the specified design space to determine if any solutions exist. An optimization is performed on any mechanisms found to determine which of the mechanism configurations is optimal with respect to the specified criteria of desirability. Simulation and analysis is then performed on the optimal mechanism to verify that it meets all specified requirements and constraints. The result of this design is a controllable residential circuit breaker than can be used in a residential load management scheme.
Determination of the Workspace of 6-DOF Parallel Manipulators
Authors: Gosselin C.
Published: June 2008

This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration in its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully parallel manipulator.
Computer-Aided Kinematic Analysis of Planar Mechanisms Based on Symbolic Pattern Matching of Independent Kinematic Loops
Authors: Chieng Wei-Hua , Hoeltzel D. A.
Published: June 2008

Based on a problem decomposition strategy and a symbolic kinematic loop pattern matching technique, a new method for planar mechanism kinematic analysis has been uncovered. Since this approach directly applies an analytical, closed form solution methodology to the planar mechanism kinematics problem, a number of significant advantages over other solution methods have been observed. Firstly, when applicable, this new approach requires significantly less cpu time as compared with traditional numerical methods, making timely mechanism animation feasible. Secondly, the new approach eliminates the effect of computer truncation error, thereby eliminating numerical approximation errors. Finally, it can be used to search for initial positions of planar mechanism with specified dimensions, thereby enabling automatic mechanism sketching.
Primary Workspace of Industrial Robots With Roll-Pitch-Yaw Wrists
Authors: Yang D. C. H. , Lin E. Y. , Cheng S. Y.
Published: June 2008

This paper presents a new method to identify the primary workspace of six-link industrial robots with Roll-Pitch-Yaw wrists in conjunction with four basic types of regional structures: the Cartesian, the cylindrical, the spherical and the articulated. The approach is to divide a robot into two subsystems, the regional structure and the wrist. Each subsystem is studied independently and then reassembled via a vector field analysis. Geometrical criteria are established to determine whether or not the kinematic connection between the wrist and the regional structure is valid. Conditions for a robot to access a point from a specified direction are derived first. The primary workpoints are then identified. Consequently, the boundaries of the primary workspaces (on the conservative side) of robots with Roll-Pitch-Yaw wrists, for the first time, can be analytically drawn. Some regional structures adopted in commercial robots which differ slightly from the standard ones are also included.
Parameter Sensitivity Analysis in Two-Level Design Optimization
Authors: Li W.-C. , Azarm S.
Published: June 2008

Parameter sensitivity analysis of a two-level design optimization problem can be decomposed into two levels. In the first-level, the sensitivities of the subproblems are calculated separately. In the second-level, the sensitivities obtained for the first-level subproblems are coordinated to obtain the overall sensitivity information. Using this approach, we cannot only obtain the overall effect that a small change in a parameter has on the optimum solution of a problem (or system) but also its local effects on the subproblems (or subsystems). A simple two-bar truss example demonstrates the approach.
Compromise: An Effective Approach for Designing Composite Conical Shell Structures
Authors: Fuchs W. J. , Karandikar H. M. , Mistree F. , Eschenauer H. A.
Published: June 2008

The layout of fiber composite structures compared to that of structures made from conventional homogeneous isotropic materials is far more difficult, because a fiber composite (laminate) is built up of several unidirectional layers (UD-layers) with fibers set at different angles. A contribution to the structural analysis and preliminary design of a fiber-reinforced conical shell is made in this paper. The equations of the membrane theory are used for analyzing the shell behavior. The design, with the objective of obtaining minimal deformation at minimal weight, subject to a set of failure constraints, is achieved by formulating and solving a compromise Decision Support Problem. Some designs of a fiber reinforced conical shell subjected to pressure load and temperature are presented.
A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems
Authors: Lankarani H. M. , Nikravesh P. E.
Published: June 2008

A continuous contact force model for the impact analysis of a two-particle collision is presented. The model uses the general trend of the Hertz contact law. A hysteresis damping function is incorporated in the model which represents the dissipated energy in impact. The parameters in the model are determined, and the validity of the model is established. The model is then generalized to the impact analysis between two bodies of a multibody system. A continuous analysis is performed using the equations of motion of either the multibody system or an equivalent two-particle model of the colliding bodies. For the latter, the concept of effective mass is presented in order to compensate for the effects of joint forces in the system. For illustration, the impact situation between a slider-crank mechanism and another sliding block is considered.
Trajectory Planning Using the Ferguson Curve Model and Curvature Theory of a Ruled Surface
Authors: Ryuh B. S. , Pennock G. R.
Published: June 2008

The trajectory of a robot end-effector is completely described by a ruled surface and a spin angle about the ruling of the ruled surface. In this way the differential properties of motion of the end-effector are obtained from the well-known curvature theory of a ruled surface. The robot can then be programmed so that the end-effector will follow the prescribed trajectory with high accuracy. In the case where the ruled surface cannot be described by an explicit analytic function, the ruled surface may be represented by a geometric modeling technique. Since a ruled surface can be expressed in terms of a single parameter, a curve generating technique is used to represent the ruled surface. The technique presented in this paper is the Ferguson curve model which guarantees that the trajectory will pass through all of the set points and will have curvature continuity at each set point. To illustrate the proposed method of robot trajectory planning, a practical example is included in the paper.
Coupler-Point-Curve Synthesis Using Homotopy Methods
Authors: Tsai Lung-Wen , Lu Jeong-Jang
Published: June 2008

A numerical method called “Homotopy Method” (or Continuation Method) is applied to the problem of four-bar coupler-curve synthesis. We have shown that: for five precision points, the “General Homotopy Method” can be applied to find the link lengths of number of four-bar linkages, and for nine precision points, a heuristic “Cheater’s Homotopy” can be applied to find some four-bar linkages. The nine-coupler-points synthesis problem is highly non-linear and highly singular. We have found that Newton-Raphson’s method and Powell’s method tend to converge to the singular solutions or do not converge at all, while the Cheater’s Homotopy always finds some non-singular solutions although sometimes the solutions may be complex.
A Substructure Technique for Dynamics of Flexible Mechanical Systems With Contact-Impact
Authors: Wu S.-C. , Haug E. J.
Published: June 2008

A substructure synthesis method is proposed to account for contact-impact effects in flexible components of mechanical systems. Components that may come into contact are divided into substructures, on each of which local deformation modes are defined to describe deformation fields of components. Constraint modes and fixed interface normal modes are used to account for elastic deformation within each substructure. A constraint addition-deletion technqiue is used to determine when contact occurs, account for the effect of contact constraints during the period of contact, and delete constraints after the completion of the contact event. Lagrange multipliers associated with the contact constraints, which represent contact forces, are used to determine the time of separation of contacting nodes. Use of the method is illustrated for longitudinal and transverse impact of elastic bars.
Design of Pitch Cones for Face-Hobbed Hypoid Gears
Authors: Litvin F. L. , Chaing W.-S. , Lundy M. , Tsung W.-J.
Published: June 2008

The authors proposed a method that allows the relations between the pitch cone angles and spiral angles to be determined directly. These relations are represented by a system of three nonlinear equations that are derived from: (a) conditions of tangency of the pitch cones and (b) the specific location of the head-cutter that generates hypoid gears with face-hobbed teeth of uniform depth. A computer program for the determination of pitch cone parameters has been developed. Equations have also been derived that allow to determine the location of apices of pitch cones with respect to the line of shortest distance, the coordinates of point of tangency of the pitch cones and the orientation of the plane that is tangent to the pitch cones. The proposed method is illustrated with a numerical example.
A Study on Timing Belt Noise (How to Reduce Resonant Noise)
Authors: Koyama T. , Watanabe K. , Nagai K. , Kagotani M.
Published: June 2008

Tow methods of suppress the resonant noise of timing belts are proposed. One method is to vary the belt tension periodically by the use of an eccentric pulley and the other method is to vary the mass density of the belt. It was experimentally confirmed that the resonant noise of timing belts is reduced by about 10 dB by the use of each method.
A New Gears Profile Having Zero Relative Curvature at Many Contact Points (LogiX Tooth Profile)
Authors: Komori T. , Ariga Y. , Nagata S.
Published: June 2008

We have successfully developed a tooth profile which enables a spur gear having zero relative curvature at contact points under the engagement through the concave/convex pattern of contact and further enables a single flank of the tooth profile to have the infinite number of points where the relative curvature and specific sliding are zero values. We have given a name of “LogiX” to this tooth profile. A W-N (Wildhaber-Novikov) tooth profi¨le has been known as that having the concave/convex pattern of contact. The tooth profile, however, is applied only to a helical gear due to its feature of a point contact. While, on the LogiX tooth profile, an improvement has been made so that a pair of spur gears having the tooth profile may contact each other through the concave/convex pattern of a line-contact which cannot be achieved by the W-N tooth profile. Therefore, the LogiX tooth profile has realized a spur gear whose surface durability is as high as that of the W-N tooth profile. Since the results of durability tests show slightly higher than an involute one, it is expected that a new type heavy duty gear of this tooth profile puts into practical use. Furthermore, the tooth profile will have the possibility of creating the new era in the history of tooth profile theory.
Geometry Conditions for Good Power Capacity in a V-Ribbed Belt Drive
Authors: Hansson H.
Published: June 2008

Important considerations when designing a V-ribbed belt drive for maximum power transmission and service life are discussed. Owing to different pulley diameters and wear of the belt, the wedge angle of the belt changes and the pressure distribution between belt and pulley differs. In this paper a method for calculating the wedge angle of the belt as a function of curvature is presented. Calculations show that the pressure distribution depends strongly on pulley diameter. Moreover, the pressure distribution between the belt and the pulley is shown to affect the torque capacity in a drive to a large extent.
Nonlinear Axial Stiffness Characteristics of Axisymmetric Bolted Joints
Authors: Grosse I. R. , Mitchell L. D.
Published: June 2008

A critical assessment of the current design theory for bolted joints which is based on a linear, one-dimensional stiffness analysis is presented. A detailed nonlinear finite element analysis of a bolted joint conforming to ANSI standards was performed. The finite element results revealed that the joint stiffness is highly dependent on the magnitude of the applied load. The joint stiffness changes continuously from extremely high for small applied loads to the bolt stiffness during large applied loads, contrary to the constant joint stiffness of the linear theory. The linear theory is shown to be inadequate in characterizing the joint stiffness. The significance of the results in terms of the failure of bolted joints is discussed. A number of sensitivity studies were carried out to assess the effect of various parameters on the axial joint stiffness. The results revealed that bending and rotation of the joint members, interfacial friction, and the bolt/nut threading significantly influence the axial stiffness characteristics of the bolted joint. The two-dimensional, axisymmetric finite element model includes bilinear gap elements to model the interfaces. Special orthotropic elements were used to model the bolt/nut thread interaction. A free-body-diagram approach was taken by applying loads to the outer diameter of the joint model which correspond to internal, uniformly distributed line-shear and line-moment loads in the joint. A number of convergence studies were performed to validate the solution.
Geometric Synthesis of Manipulators Using the Monte Carlo Method
Authors: Rastegar J. , Fardanesh B.
Published: June 2008

A new approach to the solution of problems of geometric synthesis of manipulators is presented. It utilizes the Monte Carlo method, is general, and can be applied to any type of manipulator. Joint motion limitations can be included. The task space may have any arbitrary geometry. The allowable manipulator installation space is determined. Synthesis for a specified number of possible configurations (branches), and optimization of task space geometry are discussed.
Generation of Manipulator Workspace Boundary Geometry Using the Monte Carlo Method and Interactive Computer Graphics
Authors: Rastegar J. , Perel D.
Published: June 2008

The Monte Carlo method is used to generate the workspaces of manipulators, and the boundary surfaces that separate subspaces having different numbers of configurations (branches); i. e., the singularity surfaces. The method is shown to be simple and readily implementable. It does not use any inverse calculations, and no direct computation of points of singularity is required. The method is naturally suitable for graphical presentation of the geometry of the boundary (singularity) surfaces. The boundary surfaces can be analytically approximated. Limitations on joint motions may be included.
On the Galloway-Type of Spatial Mechanisms
Authors: Rastegar J.
Published: June 2008

The Galloway mechanism is a plane four-bar, drag-link-type linkage with one pair of equal-length shorter links, and one pair of equal-length longer links, forming a rhomboid geometry. The short links constitute the frame and the input links. In a Galloway mechanism, two full rotations of the input link result in a single rotation of the output link. In this paper, the Galloway mechanism is analyzed and the rules governing its motion are found. The conditions necessary for the existence of a Galloway-type spatial mechanism are then determined. As an example, the necessary relationships between the geometric parameters of a spatial RRRSR mechanism are derived. A numerical example is included.
Comparison of Methods for Determining Screw Parameters of Finite Rigid Body Motion From Initial and Final Position Data
Authors: Fenton R. G. , Shi Xiaolun
Published: June 2008

Five methods for determining screw parameters of finite rigid body motion, using position data of three noncollinear points, are compared on the basis of their efficiency, accuracy, and sensitivity to data error. It is found that the method based on Rodrigues’ Formula (Bottema and Roth’s method) is the most efficient. Angeles’ method and Laub and Shiflett’s method provide approximately the same level of accuracy, which is superior to that of the other methods. In terms of sensitivity, Bottema and Roth’s method is preferable. On the basis of this study it is recommended that Bottema and Roth’s method be used if uncertainty exists in the data, since it can provide a solution efficiently, accurately and it is the least sensitive to data error.
A Mechanics-Based Computer Algorithm for Displaying the Margin of Static Stability in Four-Legged Vehicles
Authors: Davidson J. K. , Schweitzer G.
Published: June 2008

The subject of this paper is the application of screw-mechanics and geometry to determine the potential upset of computer-controlled four-legged vehicles which are under development for use in very uneven terrain by the European construction and forestry industries. The margin of static stability is measured using normalized values for virtual power, each value corresponding to the motion about an axis of rotation which is associated with one mode of potential overturning. Static stability is treated for spatial positioning of the feet and for both three and four feet in contact with the ground. External reaction loads at the tool are included, and the load from a tethering cable-which arrangement can also be included. The inertial loads from a heavy tool, such as an excavating arm, can be included in a quasi-static manner. The values for normalized virtual power are then related to a geometrical description of stability of the vehicle as if it were operating on level ground. Recommendations are made for visually displaying the geometrical description to the operator of the machine. The required measurements of force and position are listed.
An Integrated System for Design of Mechanisms by an Expert System—DOMES: Theory
Authors: Yang B. , Datseris P. , Datta U. , Kowalski J.
Published: June 2008

Methodologies have been developed and implemented in LISP and OPS-5 languages which address type synthesis of mechanisms. Graph theory and separation of structure from function concepts have been integrated into an expert system called DOMES (Design Of Mechanism by an Expert System) to effectively implement the following three activities: (1) enumeration of all nonisomorphic labelled graphs; (2) identification of those graphs which satisfy structural constraints; (3) sketching of a mechanism corresponding to a given graph. Developed theories and algorithms are applied to a Robot Gripper design [19] and a Variable Stroke Piston Engine design [16]. The results from these two applications indicate that the automated techniques effectively identify all previously obtained solutions via manual techniques. Additional solutions are also identified and several errors of the manual process are detected. The developed methodologies and software appear to perform a complete and unbiased search of all possible candidate designs and are not prone to the errors of the manual process. Other important features of DOMES are: (1) it can learn and reason, by analogy, about a new design problem based on its experience of the problems previously solved by the system; (2) it has the capability to incrementally expand its knowledge base of rejection criteria by converting into LISP code information obtained through a query-based interactive session with a human designer; (3) it can select the set of rejection criteria relevant to a design problem from its knowledge base of rejection criteria. These procedures could become a powerful tool for design engineers, especially at the conceptual stage of design.
Kinematic Inversion of Parallel Manipulators in the Presence of Incompletely Specified Tasks
Authors: Gosselin C. , Angeles J.
Published: June 2008

In this paper, the kinematic inversion of redundant parallel manipulators in the presence of incompletely specified tasks is formulated as an optimization problem. The performance index used is the condition number of the Jacobian matrix of the manipulator which is a measure of Jacobian invertibility. In order to optimize this index along a partially prescribed Cartesian trajectory, the concept of trajectory map is introduced. It is also shown that the optimum value of the free parameter that minimizes the condition number is not a continuous function of the prescribed Cartesian coordinates. An on-line algorithm producing continuous joint histories is then discussed. This method has been implemented and tested, as illustrated with the results presented here.
A Computer-Based Methodology for the Form Synthesis and Optimal Design of Robot Manipulators
Authors: Manoochehri S. , Seireg A. A.
Published: June 2008

The study reported in this paper deals with the development of a generalized computer-based methodology for the form synthesis and optimal design of robot manipulators. The developed computer program to implement the methodology operates in two separate modes. The first deals with the synthesis of user defined topologies and in the second mode, the designer provides only the required task, then the program will generate optimum manipulator configuration by systematic evaluation and ranking of plausible alternatives. The methodology simultaneously incorporates kinematic and dynamic synthesis as well as optimal actuation and stress analysis in an integrated design process. The procedure relies on the systematic composition of manipulator configurations from tabulated basic elements. The optimization strategy for synthesis and control utilizes a dynamic programming approach which makes it possible to select the optimum parameters in a stage-wise manner without sacrificing the interactions inherent in such highly coupled nonlinear systems.
Dynamic Analysis of a Valve Spring With a Coulomb-Friction Damper
Authors: Paranjpe R. S.
Published: June 2008

The dynamic behavior of a distributed parameter valve spring with Coulomb damping has been modeled. Such a spring is described by a nonlinear, nonhomogeneous wave equation. This equation is solved using an explicit finite difference scheme. Some sample results are presented. The results of the finite difference scheme are compared with the results of an analytical solution for zero damping. The two compare very well. The spring is also modeled using an equivalent viscous damping coefficient. The results of this analysis are compared with those of the Coulomb damping analysis.
The Stratified Representation of Mechanisms
Authors: Fang W. E. , Freudenstein F.
Published: June 2008

A new method for the representation of the kinematic structure of mechanisms has been proposed. This scheme is an order-of-magnitude faster in enumerating mechanisms than the conventional characteristic-polynomial approach. Moreover, unlike the traditional approach, it never fails to identify a mechanism and all structural information relating to the mechanism can be retrieved from this representation. Classification of mechanisms based on structural characteristics is built-in as well. Using this method, the graphs of approximately one million kinematic chains have been generated and stored in a computer.
Parallel Processing for Real-Time Dynamic System Simulation
Authors: Hwang R. S. , Bae D. S. , Kuhl J. G. , Haug E. J.
Published: June 2008

A parallel processing algorithm based on the recursive dynamics formulation presented in a companion paper [1] is developed for multiprocessor implementation. Lagrange multipliers associated with cut-joint constraints for closed loop systems are eliminated, resulting in a minimal set of equations of motion. Concurrent generation of the system inertia matrix and the generalized force vector using the algorithm of Ref. 1 is shown to yield finer grain parallelism than earlier recursive algorithms. A new computational structure for dynamic analysis is proposed for high speed parallel processing. Real-time simulation of a vehicle is demonstrated on an eight processor parallel computer to illustrate efficiency and effectiveness of the algorithm, even for interactive operator-in-the-loop simulation.
Three-Dimensional Dynamic Simulation of Helical Compression Springs
Authors: Lin Y. Y. , Pisano A. P.
Published: June 2008

The dynamic equations for general helical springs are solved and classified according to the number of energy terms used to formulate them. Solutions of several sets of dynamic equations, each with a different number of energy terms, are compared with experimental data. It is found that at higher compression speeds the numerical solution with a traditional, fixed boundary represents a physically impossible situation. A moving boundary technique is applied to improve the numerical solution and bring it into agreement with physical reality. Since a convergence proof for a numerical algorithm for nonlinear partial differential equations with a moving boundary is not available, a grid study has been performed to demonstrate convergence. The agreement between the solutions of different grid sizes and the experimental data is taken to show that the numerical algorithm was convergent. This three dimensional spring simulation model can be used in the simulation of high-speed mechanical machinery utilizing helical springs, and in particular, for design optimization of automotive valve springs.
Transient Torque Produced in Arm Shaft of an Industrial Sewing Machine
Authors: Muramatsu N.
Published: June 2008

This study considered the effects of needle penetrating force, needle thread tightening tension, and pressing force of the presser foot on torque produced in the arm shaft of an industrial sewing machine. The results obtained are as follows. (1) Penetrating force, especially the initial triangular wave fluctuation, induces noticeable transient vibration in torque. (2) The penetrating force is considerably more transient than the pressing force. The time ratio of the duration of the penetrating force to the natural period of the motion system is close to 1. (3) Consequently, when estimating torque, it is necessary that the arm shaft of the thread take-up lever and needle bar mechanism motion system be considered as elastic. On the other hand, the arm shaft of the feed mechanism motion system can be treated as a rigid body.
Solving a Planar Four-Bar Design Problem Using Continuation
Authors: Morgan A. P. , Wampler C. W.
Published: June 2008

The problem of synthesizing a planar 4-bar with given pivots such that the coupler curve passes through five precision points is considered. It is shown that the design parameters must satisfy a system of 4 fourth-degree polynomial equations in 4 unknowns which has at most 36 nonzero real solutions. This polynomial system is solved using a continuation method, which thereby generates the collection of all designs that meet the precision-point specification. A computer program that implements this continuation method has been tested on a number of problems. It is reliable and fast enough for the purposes of design. The approach to kinematic design represented by this work is completely general, subject only to computer-time limitations that may arise for problems with many design elements.
Modeling and Analysis of a Manipulator Joint Driven Through a Worm Gear Transmission
Authors: Mooring B. W. , May D. C. , Schulte M.
Published: June 2008

Worm gear transmissions are capable of high velocity ratios as well as redirection of rotation. Both of these features are desirable for some robot geometries. A problem has been encountered in several robot designs; however, where a self-excited vibration occurs for some configurations of the manipulator in the joint containing the worm gear. In this work, a system which exhibits this type of undesirable motion is examined. The system consists of a DC servo motor which is used to position a flexible cantilever arm through a worm gear transmission. A nonlinear model is developed to describe the motion of the system. The model is then validated by comparing the predicted response to the observed response of an experimental system. It is demonstrated that the model accurately predicts the onset of the unstable vibration. The model is then linearized and it is shown that the linear model will predict the occurrence of the instability as well.