bluuebunny/crossref_metadata_2025 huggingface dataset:
Patterns of Water, Heat, and Solute Flux through Streambeds around Small Dams
Authors: Fanelli Rosemary M. , Lautz Laura K.
Published: June 2008

Hyporheic exchange, enhanced by complex stream channel morphology, can influence biogeochemical processing in the streambed. These processes chemically alter water passing temporarily through the streambed, which eventually returns to the stream channel and can potentially affect surface water quality. To assess the degree of biogeochemical cycling induced by complex streambed morphology, we instrumented two 20‐m reaches of Red Canyon Creek, Wyoming, each containing a small log dam, with in‐stream minipiezometers and temperature data loggers. We simultaneously observed pore water geochemistry and streambed temperature dynamics in several bedforms located upstream or downstream of the dams. We modeled seepage flux into the streambed using heat transport modeling.

Upstream of the dams, low‐permeability sediments have settled out in low‐velocity pools, and enhanced anaerobic biogeochemical cycling occurred in the streambed. Rapid flux into the streambed occurred in glides immediately above the dams, where streambed temperature dynamics and geochemistry were nearly identical to the stream. In riffle sequences downstream of the dams, the streambed was oxygen rich, showed evidence of nitrification, and temperature dynamics indicated high connectivity between the streambed and the stream. Further downstream, streambed pore water geochemistry indicated ground water discharge occurring at the pool‐riffle transition. Assessing streambed biogeochemical cycling may be facilitated by coupling streambed temperature measurements with pore water geochemistry and can aid in understanding how hyporheic exchange contributes to overall stream biogeochemistry.
Surface Intersections for Geometric Modeling
Authors: Patrikalakis N. M. , Prakash P. V.
Published: June 2008

Evaluation of planar algebraic curves arises in the context of intersections of algebraic surfaces with piecewise continuous rational polynomial parametric surface patches useful in geometric modeling. We address a method of evaluating these curves of intersection that combines the advantageous features of analytic representation of the governing equation of the algebraic curve in the Bernstein basis within a rectangular domain, adaptive subdivision and polyhedral faceting techniques, and the computation of turning and singular points, to provide the basis for a reliable and efficient solution procedure. Using turning and singular points, the intersection problem can be partitioned into subdomains that can be processed independently and which involve intersection segments that can be traced with faceting methods. This partitioning and the tracing of individual segments is carried out using an adaptive subdivision algorithm for Bezier/B-spline surfaces followed by Newton correction of the approximation. The method has been successfully tested in tracing complex algebraic curves and in solving actual intersection problems with diverse features.
Optimization Modelling and Optimal Layouts of Heterogeneous, Thick-Walled, Chilled Cast-Iron Rollers
Authors: Eschenauer H. A. , Bremicker M.
Published: June 2008

The design and material selection of chilled cast-iron rollers depends on their field of application. In special applications, they are subjected to permanent changes of temperature distributions. Whereas unalloyed roller materials are relatively temperature-resistant, this characteristic does not follow for highly alloyed, wear-resistant roller materials. In the case of temperature loadings it must be attempted to reduce the thermal stresses at the critical points of the roller. This paper gives a survey of the optimization modelling whose goal is to minimize weight and stress simultaneously as well as to fulfill numerous constraints. Some of the optimal layouts will be presented as results of the solution of a multicriteria design optimization problem.
Force Distribution in Walking Vehicles
Authors: Kumar V. , Waldron K. J.
Published: June 2008

This paper addresses the problem of the appropriate distribution of forces between the legs of a legged locomotion system for walking on uneven terrain. The legs of the walking machine and the terrain form closed kinematic chains. The system is statically indeterminate and an optimal solution is desired for force control of the legs. In addition, as unisense force limitations are imposed on the wrenches acting at the feet, it is important to be able to determine for any given configuration whether or not a set of valid contact forces can be found which will ensure the stability of the vehicle. Fast and efficient algorithms to solve these problems have been developed. The trade-off between computational simplicity and optimality makes it necessary to resort to suboptimal algorithms. In particular, schemes based on the Moore-Penrose Generalized Inverse, or the pseudo inverse, and linear programming were investigated. An active compliance control scheme with varying leg compliances is shown to be a suitable paradigm for control. A variation of the linear programming technique, that is well-suited to the problem of predicting instability in the vehicle, is also presented.
Spatial Dynamics of Deformable Multibody Systems With Variable Kinematic Structure: Part 1—Dynamic Model
Authors: Chang C. W. , Shabana A. A.
Published: June 2008

In this paper a method for the spatial kinematic and dynamic analysis of deformable multibody systems that are subject to topology changes is presented. A pieced interval analysis scheme that accounts for the change in the spatial system topology due to the changes in the connectivity between bodies is developed. Deformable bodies in the system are discretized using the finite element method and accordingly a finite set of deformation modes is employed to characterize the system vibration. Even though there are infinitely many arrangements for deformable body axes, computational difficulties may be encountered due to the use of a limited number of deformation modes. Therefore, the deformable body references have to be carefully selected, and accordingly as the system topology changes, new bases for the configuration space have to be identified. In order to guarantee a smooth transition from one configuration space to another, a set of spatial interface conditions or compatibility conditions that are formulated using a set of nonlinear algebraic equations are developed and solved in this paper. The solution of these equations uniquely define the spatial configuration of the deformable multibody system after the change in the system kinematic structure.
A New Dynamic Basis Algorithm for Solving Linear Programming Problems for Engineering Design
Authors: Wang Y. , Sandgren E.
Published: June 2008

A new linear programming algorithm is proposed which has significant advantages compared to a traditional simplex method. A search direction is generated along a common edge of the active constraint set. This direction is followed in order to identify candidate constraints and to modify the current basis. The dimension of the basis matrix begins with a single element and dynamically increases but remains less than or equal to the number of design variables. This is true regardless of the number of inequality constraints present including upper and lower bounds. The proposed method can operate equally well from a feasible or infeasible point. The pivot operation and artificial variable strategy of the simplex method are not used. Examples are presented and results are compared to those generated by a traditional revised simplex algorithm. Extensions are presented for both exterior and interior versions of the approach.
Existence Criteria for Over-Constrained Mechanisms: An Extension of Motor Algebra
Authors: Sugimoto K.
Published: June 2008

The new concept of a mobile screw space is introduced in this paper. A mobile screw space is a set of motors for which the outer product of any two arbitrary elements belongs to the original set. It is shown that the condition for the existence of almost all existing over-constrained mechanisms is related to the mobile screw space, that is, all joint motors of the mechanism either belongs to a mobile screw space or belong to a space which is given as the sum of mobile spaces. Determining an over-constrained mechanism on the basis of this condition makes it possible to generate many mechanisms, including most presently known over-constrained mechanisms.
Experimental Model Validation for a Flexible Robot With a Prismatic Joint
Authors: Pan Ye-Chen , Ulsoy A. Galip , Scott R. A.
Published: June 2008

In [1] a dynamic model for flexible manipulators with prismatic joints and the solution method were presented. In this paper experiments on a spherical coordinate robot are performed to further validate the proposed dynamic model. Using the validated model, numerical simulations are performed to illustrate the coupling effects between the rigid body motions and the flexible motions, the effects of the flexible motion on a rigid body controller, and the effects of axial shortening.
Some Results in Optimization of Nonhierarchic Systems
Authors: Pan J. , Di´az A. R.
Published: June 2008

Practical difficulties that are inherent to the solution of optimization problems by nonhierarchic decomposition are discussed. The study is motivated by design problems that require the optimization of a system comprised of several, tightly coupled subsystems or components. A strategy for the optimization of such problems is presented. Examples are provided for illustration.
Optimization of the Wrist Pin End of an Automobile Engine Connecting Rod With an Interference Fit
Authors: Sarihan Vijay , Song Ji Oh
Published: June 2008

Current design procedures for complicated three-dimensional structural components with component interactions may not necessarily result in optimum designs. The wrist pin end design of the connecting rod with an interference fit is governed by the stress singularity in the region where the wrist pin breaks contact with the connecting rod. Similar problems occur in a wide variety of structural components which involve interference fits. For a better understanding of the problems associated with obtaining optimum designs for this important class of structural interaction only the design problems associated with the wrist pin end of the rod are addressed in this study. This paper demonstrates a procedure for designing a functional and minimum weight wrist pin end of an automobile engine connecting rod with an interference fit wrist pin. Current procedures for Finite Element Method (FEM) model generation in complicated three-dimensional components are very time consuming especially in the presence of stress singularities. Furthermore the iterative nature of the design process makes the process of developing an optimum design very expensive. This design procedure uses a generic modeler to generate the FEM model based on the values of the design variables. It uses the NASTRAN finite element program for structural analysis. A stress concentration factor approach is used to obtain realistic stresses in the region of the stress singularity. For optimization, the approximate optimization strategy in the COPES/CONMIN program is used to generate an approximate design surface, determine the design sensitivities for constrained function minimization and obtain the optimum design. This proposed design strategy is fully automated and requires only an initial design to generate the optimum design. It does not require analysis code modifications to compute the design sensitivities and requires very few costly NASTRAN analyses. The connecting rod design problem was solved as an eight design variable problem with five constraints. A weight reduction of nearly 27 percent was achieved over an existing design and required only thirteen NASTRAN analyses. It is felt that this design strategy can be effectively used in an engineering environment to generate optimum designs of complicated three-dimensional components.
A Study on Timing Belt Noise (Theoretical Analysis for Forced Transverse Vibration of Timing Belt With Parametric Excitation)
Authors: Watanabe K. , Koyama T. , Nagai K. , Kagotani M.
Published: June 2008

A theoretical analysis is made for two kinds of noise reduction methods of timing belts. The methods are confirmed experimentally in a companion paper [1]. Modeling the traveling belt as a string with parametric excitation in tension and density, we obtain an approximate solution for the amplitude of the transverse vibration and carry out some numerical computations for the response of the belt. It is shown that the maximum amplitude of the transverse vibration at resonance is reduced by the two kinds of parametric excitation. The method of variable tension suppresses the maximum amplitude almost for all modes of vibration at resonance and that of the variable density is effective for higher modes except the first mode at resonance.
Singular Conditions and Solutions of the Standard Triad Displacement Equation
Authors: Lin Chuen-Sen , Erdman A. G.
Published: June 2008

In the dimensional synthesis of a standard planar triad, if the prescribed angular displacements of two of the three links are the same at all precision positions or the prescribed angular displacements of one link are zero at all precision positions, the standard triad displacement equation will not yield a practical solution: a triad having all links with finite lengths. The displacement equation may also fail to generate a practical solution triad in case that the freely chosen angular displacement of one link equals to zero, or equals to the prescribed angular displacement of another link at the same precision position. In this paper, the special cases in the dimensional synthesis of a standard triad are discussed in detail, the types of triads which can generate the motions corresponding to the special cases are listed, and the solution methods to solve the displacement equations of the special types of triads are developed. Finally a numerical example is given to show the application of one of the special types of triad in the dimensional synthesis of an eight-bar linkage.
Generalized Modeling of Dynamic Cam-follower Pairs in Mechanisms
Authors: Bagepalli B. S. , Haskins T. L. , Imam I.
Published: June 2008

This paper deals with the application of homogeneous (4 × 4) transformations to the generalizing modeling of cam-follower pairs. The procedure adopted is generic, in that it suggests a method of incorporating the modeling of cam-follower pairs in a general purpose program, such as MAP (Mechanism Analysis Program, © General Electric Co.) capable of solving the dynamics of multibody systems, in which any of the bodies could be cams, or followers. This development covers both 2D and 3D cam-follower pairs: XY cams, rotary cams, and drum cams. The cams could be dynamic—with single, or two surfaces (or tracked), with the possibility of impacts between the follower and these surfaces, or, kinematic, with the follower being guided exactly in a slot. This generalized procedure allows one to model several cam-follower pairs in a multibody dynamic system. This is useful in studying, for instance, the dynamic effects that tend to bounce a follower off of a cam surface, the contact force generated, etc. The procedure, also, just as easily, allows for the easy studying of the effects of varying the cam surface profile. Several examples have been tried, and some correlations have been obtained with experimental observations.
Design of Keratorefractive Surgical Procedures: Radial Keratotomy
Authors: Bryant M. R. , Velinsky S. A.
Published: June 2008

By surgically incising a patient’s cornea, an ophthalmologist can reduce or eliminate the patient’s myopia (nearsightedness). Although one such keratorefractive produre, known as radial keratotomy, is a common practice among some ophthalmologists, there is presently no comprehensive or universally accepted method that a surgeon can use to determine how to perform the operation to exactly eliminate a patient’s refractive error. In this paper, a general methodology for designing radial keratotomy procedures that determines the optimal incision geometry on a patient-by-patient basis is presented. This approach is based on coupling a transversely isotropic finite element model of the human cornea to an optical model of the entire eye. The resulting incision geometry obtained from each design formulation not only eliminates the myopic error but yields the global minimum of the objective function.
A Global Performance Index for the Kinematic Optimization of Robotic Manipulators
Authors: Gosselin C. , Angeles J.
Published: June 2008

In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.
Flexible Semi-Empirical Models for Hydraulic Flow Control Valves
Authors: Handroos H. M. , Vilenius M. J.
Published: June 2008

Low-order nonlinear models for proportional two-way and simple three-way flow control valves are developed and subjected to experimental verification. The models are postulated in the semi-empirical manner, trying to overcome the most typical problems in modelling fluid power valves, e.g., the influence of constructional differences and the difficulty of identifying the parameter values.
Dynamic Modeling of Systems With Translating Components
Authors: Garcia Reynoso A. , Seering W.
Published: June 2008

This paper summarizes a method for modeling the vibration response of mechanical systems whose configuration may vary during operation. A model of adjacent elements which experience relative translational motion is developed. System Differential equations are derived and then transformed to accept as input angular acceleration rather than torque information at the actuator shafts. A technique for determining this angular acceleration information from optical encoder signals is described. Finally, predicted and actual vibration response for a representative system, a cartesian robot, are presented and compared.
Enumeration of Singular Configurations for Robotic Manipulators
Authors: Lipkin H. , Pohl E.
Published: June 2008

Kinematic singularities are important considerations in the design and control of robotic manipulators. For six degree-of-freedom manipulators, the vanishing of the determinant of the Jacobian yields the conditions for the primary singularities. Examining the vanishing of the minors of the Jacobian yields further singularities which are special cases of the primary ones. A systematic procedure is presented to efficiently enumerate all possible singular configurations. Special geometries of representative manipulators are exploited by expressing the Jacobian in terms of vector elements. In contrast to using a joint-angle space approach, the resulting expressions yield direct physical interpretations.
A Sequential Linearization Approach for Solving Mixed-Discrete Nonlinear Design Optimization Problems
Authors: Loh Han Tong , Papalambros P. Y.
Published: June 2008

Design optimization models of often contain variables that must take only discrete values, such as standard sizes. Nonlinear optimization problems with a mixture of discrete and continuous variables are very difficult, and existing algorithms are either computationally intensive or applicable to models with special structure. A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables. It involves solving a sequence of mixed-discrete linear approximations of the original nonlinear model. In this article, a review of previous approaches is followed by description of the resulting algorithm, its convergence properties and limitations. Several illustrative examples are given. A sequel article presents a detailed algorithmic implementation and extensive computational results.
A Study on the Tooth Geometry and Cutting Machine Mechanisms of Spiral Bevel Gears
Authors: Fong Z. H. , Tsay Bill Chung-Biau
Published: June 2008

The tooth geometry and cutting machine mechanisms of spiral bevel gears are investigated. Based on the kinematics of titled head cutter, machine cradle, sliding base and work head, the matrix presentation of spiral bevel gear’s tooth geometry are developed. The relations between the parameters of the proposed mathematical model and the machine settings of existing spiral bevel gear cutting machines are also investigated. The tilt of head cutter axis, motion of generation, helical motion of sliding base, and nongenerating cutting of spiral bevel gears are taken into consideration. An example is given to illustrate the application of the proposed mathematical model.
Computer Aided Geometric Design of Line Constructs
Authors: Ravani B. , Wang J. W.
Published: June 2008

This paper develops a mathematical foundation for Computer Aided Design (CAD) of sculptured shapes based on line geometry. First, a new representation is presented for a line based on Plu¨cker coordinates that would allow specification of a line segment (rather than an infinite line) in an elegant manner and suitable for computational purposes. Then, methods are presented for geometric design of shape patches (here referred to as line constructs) by interpolating or approximating a set of control lines (rather than control points) using ruled surfaces, line congruences, and line complexes. The methods presented are general and allow utilization of different basis functions such as Be´zier, Cardinal, and B-spline bases. As Computer Aided Manufacturing (CAM) application of the theory, methods are developed for generation of offsets of ruled surfaces useful in Numerical Control (NC) milling and tool motion generation in the Wire Cut Electric Discharge Machining (EDM) operation.
The Role of Meta-Level Inference in Problem-Solving Strategy for a Knowledge-Based Dynamics Analysis Aid
Authors: Brown D. R. , Leifer L. J.
Published: June 2008

The explicit representation of knowledge in knowledge-based analysis tools may help designers by improving the nature of their interaction with the tools. This work shows how meta-level inference makes knowledge-based architectures feasible for building engineering analysis tools, particularly in the field of dynamics. Meta-level inference improves performance and makes control knowledge explicit so that it may be more easily understood by humans than if it were embedded in domain knowledge. Also shown are some methods which further improve the performance of meta-level representation and its ability to represent control knowledge.
Influence of Linear Profile Modification and Loading Conditions on The Dynamic Tooth Load and Stress of High-Contact-Ratio Spur Gears
Authors: Lee Chinwai , Lin Hsiang Hsi , Oswald Fred B. , Townsend Dennis P.
Published: June 2008

This paper presents a computer simulation for the dynamic response of high-contact-ratio spur gear transmissions. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented in this paper examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. This paper shows that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High-contact-ratio gears were found to require less modification than standard low-contact-ratio gears. High-contact-ratio gears are more adversely affected by excess modification than by under modification. In addition, the optimal profile modification required to minimize the dynamic load (hence the contact stress) on a gear tooth differs from the optimal modification required to minimize the dynamic root (bending) stress. Computer simulation can help find the design tradeoffs to determine the best profile modification to satisfy the conflicting constraints of minimizing both the load and root stress in gears which must operate over a range of applied loads.
Performance of an Orbiting Flexible Mobile Manipulator
Authors: Modi V. J. , Chan J. K.
Published: June 2008

This paper presents a Lagrangian formulation for studying the dynamics and control of the Space Station based Mobile Servicing System (MSS) for a particular case of in-plane libration and maneuvers. The simplified case is purposely considered to focus on the effects of structural and joint flexibilities of the MSS on the complex interactions between the station and manipulator dynamics during slewing and translational maneuvers. The response results suggest that under critical combinations of parameters, the system can become unstable. During maneuvers, the deflection of the MSS can become excessive, leading to payload positioning error and the librational disturbance can also be significant. A linear quadratic regular is designed to simultaneously control the deflection of the manipulator and maintain the station at its operating configuration.
A Contribution to Multi-Axis Robot Contouring Accuracy Analysis: Modeling, Simulation, and Evaluation
Authors: Lee Ming-Yih , Holt T. , Sturm A. J.
Published: June 2008

A new way of interpreting the 3D dynamic contouring errors attributed to a multi-axis robot system based on a relaxed performance measure was introduced. Generic contouring error models were derived for evaluating path following performance for planar and spatial contours. Estimated errors were then correlated to experimental tracking test results. Finally, an overall robot contouring performance budget was mapped into joint domain dynamics matching criteria which considered to be more meaningful from a control standpoint.
An Algorithm of Topological Ordering for Unique Representation of Graphs
Authors: Kim Jeong Tae , Kwak Byung Man
Published: June 2008

An algorithm of topological ordering of vertices is proposed for generating a unique edge list of a given graph, and used for the isomorphism test. This also makes it possible to find the sets of similar vertices and edges of the graph. This is applied to the graphs representing kinematic chains.
Experimental Verification of Critical Speed Ranges for Elastic Closed Loop Linkage Systems
Authors: Nagarajan S. , Turcic D. A.
Published: June 2008

In this work critical speed ranges are determined and verified for an elastic four bar crank rocker mechanism where all links are modeled as elastic members. The procedure used for the dynamic stability analysis is described in Nagarajan and Turcic (1991). The speed range of interest where the stability analysis is performed is 195–390 rpm. The values of the critical speeds obtained in the above speed range are then verified using independent theoretical and experimental methods of analysis. The steady state strain response is obtained both theoretically and experimentally for a number of speeds in the speed range of 195–390 rpm. From these responses plots different strain characteristics versus operating speeds are obtained. These plots exhibit peaks in the response at certain speeds indicating that the dynamic response at these speeds reaches a local maximum value. The critical speed ranges determined are found to correspond quite closely to the speeds where the peaks occur. This indicates that the critical speed ranges are indeed speeds where the response of the system is larger when compared to neighboring speeds and that the methods of determining them are accurate for the application considered.
Canonical Impulse-Momentum Equations for Impact Analysis of Multibody Systems
Authors: Lankarani H. M. , Nikravesh P. E.
Published: June 2008

For mechanical systems that undergo intermittent motion, the usual formulation of the equations of motion is not valid over the periods of discontinuity, and a procedure for balancing the momenta of these systems is often performed. A canonical form of the equations of motion is used here as the differential equations of motion. A set of momentum balance-impulse equations is derived in terms of a system total momenta by explicitly integrating the canonical equations. The method is stable when the canonical equations are numerically integrated and it is efficient when the derived momentum balance-impulse equations are solved. The method shows that the constraint violation phenomenon, which is usually caused by the numerical integration error, can be substantially reduced as compared to the numerical integration of the standard Newtonian form of equations of motion. Examples are provided to illustrate the validity of the method.
Geometrical Criteria to Guarantee Curvature Continuity of Blend Surfaces
Authors: Pegna Joseph , Wolter Franz-Erich
Published: June 2008

Computer Aided Geometric Design (CAGD) of surfaces sometimes presents problems that were not envisioned in classical differential geometry. This paper presents mathematical results that pertain to the design of curvature continuous blending surfaces. Curvature continuity across normal continuous surface patches requires that normal curvatures agree along all tangent directions at all points of the common boundary of two patches, called the linkage curve. The Linkage Curve theorem proved here shows that, for the blend to be curvature continuous when it is already normal continuous, it is sufficient that normal curvatures agree in one direction other than the tangent to a first order continuous linkage curve. This result is significant for it substantiates earlier works in computer aided geometric design. It also offers simple practical means of generating second order blends for it reduces the dimensionality of the problem to that of curve fairing, and is well adapted to a formulation of the blend surface using sweeps. From a theoretical viewpoint, it is remarkable that one can generate second order smooth blends with the assumption that the linkage curve is only first order smooth. The geometric criteria presented may be helpful to the designer since curvature continuity is a technical requirement in hull or cam design problems. The usefulness of the linkage curve theorem is illustrated with a second order blending problem whose implementation will not be detailed here.
An Exact Optimization of Interaction Forces in Three-Fingered Manipulation
Authors: Mukherjee S. , Waldron K. J.
Published: June 2008

Manipulation with three fingers in frictional contact is known to be an underspecified problem. The minimum norm solution, also referred to as the equilibrating solution field, can be modified by superimposing a linear combination of the resulting null solutions, called the interaction force field. The modification proposed here, applicable to the three-dimensional problem, minimizes the maximum value of the friction angle at the points of contract. A grasp of maximum possible stability under a set of contact and loading conditions is hence achieved.
Forward Displacement Analysis of Parallel Mechanisms: Closed Form Solution of PRR-3S and PPR-3S Structures
Authors: Parenti-Castelli V. , Innocenti C.
Published: June 2008

The forward displacement analysis (FDA) in closed form of two classes of new parallel mechanisms derived from the Stewart Platform Mechanism (SPM) is presented in this paper. These mechanisms, when a set of actuator displacements is given, become multiloop structures of type PRR-3S and PPR-3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR-3S. Solving the FDA in closed form means finding all the possible positions and orientations of the output controlled link when a set of actuator displacements is given, or equivalently, finding all possible closures of the corresponding structure. The closed form analysis of the PRR-3S and PPR-3S structures here presented results in algebraic equations in one unknown of degree 16 and 12, respectively. Hence 16 and 12 closures of the corresponding structures can be obtained. Numerical examples confirm these new theoretical results.
A Complete Notation for Dual Velocity
Authors: Fischer I. S.
Published: June 2008

A notation is developed which specifies a dual velocity without ambiguity. The point of interest, the moving body, the reference body, and the system of unit vectors in which a dual velocity is expressed are all clearly indicated. The equivalence between the equation of transformation and the coordinate-transformation matrix formulation is shown. Equations are developed to enable calculation of the dual velocity at a point in a body given the dual velocity at any other point, to change the system of unit vectors in which a dual velocity is expressed, and to calculate relative velocities. Use of these equations is demonstrated in an example using the spatial four-bar mechanism which is specialized to the Cardan joint and the wobble-plate mechanism, and the effect of some tolerance errors on output velocity is shown.
Profile Synthesis and Kinematic Analysis of Pure Rolling Contact Gears
Authors: Wagner M. J. , Ng W. F. , Dhande S. G.
Published: June 2008

The kinematic analysis of a type of gearing which allows for power transmission between shafts with pure rolling contact is presented. This proposed gearing is helical and exhibits theoretical point contact. Comparisons are made between the proposed gearing and conventional types such as involute gearing and Wildhaber-Novikov circular arc gearing. The analysis of the specific proposed profile includes derivation of surface normal, pressure angle, and surface curvature. Curvatures are used to predict possible interference between mating gear surfaces. A curve showing allowable values for the tooth profile parameters is included.
Description of Machine Tool Errors Using Screw Coordinates
Authors: Ziegert J. C. , Olson D. G. , Datseris P.
Published: June 2008

The kinematic behavior of a mechanism may be modeled using a number of different formalisms. In this paper, the description of machine tool errors is examined using screw coordinates. The six components of error associated with each axis motion, three rotational errors about the three coordinate axes and three translational errors of the origin along the coordinate axes, are shown to be identically the six components of an “error twist,” or screw displacement. This “error twist” is a motor, and the six components of the motor are, in general, functions of the axis position. Thus, the “error twist” is a motor valued function of a scalar variable which describes axis errors in an extremely compact form. Furthermore, this approach allows clearer insights into errors which arise due to the Abbe´ effect. Using screw-coordinates to describe the machine errors, it becomes clear that the so-called Abbe´ errors cannot be eliminated in the general case, even if the tool point is collinear with the machine scale. However, the relative importance of these errors can be easily determined since the location of the instantaneous axis of rotation is easily found. Expressions are developed which allow the translational components of the errors to be measured at any convenient points on the body, including differing points for each component, and properly transformed into error motions of any desired point. Finally, a method for determining the total error at the tool point due to the individual error components of each of the members is presented.
Fuzzy Ratings and Utility Analysis in Preliminary Design Evaluation of Multiple Attributes
Authors: Thurston D. L. , Carnahan J. V.
Published: June 2008

A procedure for evaluation of multiple attributes in the preliminary design stage is necessary to the development of a more formal theory and methodology of design. In this paper we prescribe, demonstrate, and compare two such techniques: fuzzy set analysis and multiattribute utility analysis. We analyze the problem of preliminary material selection for an automotive bumper beam to illustrate the application of both analytical procedures. Preliminary assessment of incommensurate performance measures of weight, cost, shape restriction, stiffness, and corrosion are made for steel and polymer composite alternatives. Fuzzy analysis readily accommodates design evaluation based on semantic assessment of relative attribute levels, although it can also employ information which is entirely numerical. In contrast, utility analysis requires considerable numerical quantification. For the example studied, the ordinal ranking of alternatives was the same for both methods. Recommendations include using fuzzy analysis in the earliest stages of preliminary design evaluation or in situations limited to semantic input from design decision makers. Utility analysis may be used in later stages of preliminary design, where numerical quantification of attribute levels is possible and when decision makers are able to assess the individual attribute utility functions in the standard way. The results of utility analysis can be used to quantify acceptable design tradeoffs between attribute levels and can be used in later stages of the iterative design process.
The Application of Curvature Theory to the Trajectory Generation Problem of Robot Manipulators
Authors: Stanisˇic´ M. M. , Lodi K. , Pennock G. R.
Published: June 2008

This paper illustrates a new application of planar curvature theory to the geometric problem of trajectory generation by a two-link manipulator. The theory yields the instantaneous speed ratio, and the rate of change of the speed ratio, which correspond to the geometry of a desired point trajectory. Separate from the purely geometric speed ratio problem (i.e., the coordination problem) is the time based problem of controlling the joint rates in order to move with the specified path variables.
Circuits and Branches of Single-Degree-of-Freedom Planar Linkages
Authors: Chase T. R. , Mirth J. A.
Published: June 2008

Improved definitions for circuits and branches of mechanisms are proposed and discussed in application to planar linkages. The difficulty of circuit and branch identification of multi-loop planar linkages is introduced. The nomenclature used by various authors is correlated with the definitions proposed here. The danger of confusing circuits with branches is illustrated by demonstrating that mechanisms satisfying published “branch” criteria may actually require disassembly to reach all desired positions, rendering them useless in practice. Furthermore, a change of branch within a circuit is shown to be irrelevant to some applications.
The Stewart Platform of General Geometry Has 40 Configurations
Authors: Raghavan M.
Published: June 2008

The Stewart platform is a six-degree-of-freedom, in-parallel linkage. It is used in automotive and flight simulators, positioning tables for assembly and robotic applications, and various other applications requiring linkages with high structural stiffness. It consists of a base link, a coupler link, and six adjustable-length legs supporting the coupler link. Each leg consists of a prismatic joint with ball-joint connections to the base and coupler, respectively. The forward kinematics problem for the Stewart platform may be stated as follows: given the values of the six prismatic joint displacement inputs to the linkage, compute the position and orientation of the coupler link. This problem may be set up as a system of nonlinear multivariate polynomial equations. We solve this problem using a numerical technique known as polynomial continuation. We show that for Stewart platforms of general geometry (i.e., platforms in which the linkage parameters are arbitrary complex numbers) this problem has 40 distinct solutions.
A Modal Analysis Solution Technique to the Equations of Motion for Elastic Mechanism Systems Including the Rigid-Body and Elastic Motion Coupling Terms
Authors: Jablokow A. G. , Nagarajan S. , Turcic D. A.
Published: June 2008

This paper presents a modal analysis solution technique for the matrix equations of motion of elastic mechanism systems including the rigid-body elastic motion coupling terms and general damping. In many cases, researchers have neglected these terms because they complicate and diminish the efficiency of the solution process. This has been justified by assuming that the terms are small and do not affect the system response. The results obtained using the techniques developed within show this is true for some, but not all mechanisms. The solution technique adds the rigid-body elastic motion coupling terms to the system mass, damping, and stiffness matrices thus allowing them to affect the system response appropriately. The resulting nonsymmetric matrices are then rewritten in first order form allowing general damping to be included in the analysis. Modal analysis techniques are utilized to solve for the steady-state response of the elastic mechanism system. Thus the methods developed in this work provide a technique for including the rigid-body elastic motion coupling terms and general damping in the equations of motion while maintaining the advantage of using efficient modal analysis techniques of finding the response of the system. A number of examples are presented that establish the validity of this approach to the solution of the matrix equations of motion for elastic mechanism systems. The results show that the rigid-body elastic motion coupling terms can become significant at higher operating speeds.
Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design
Authors: Papalambros P. Y.
Published: June 2008

Early preliminary models for optimal design problems in nonlinear programming formulations often have solutions that are constraint-bound points, i.e., the number of active constraints equals the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs, and it is desirable to identify them early in order to revise the model or to exclude the points from an active set strategy. Application of monotonicity analysis can quickly identify constraint-bound candidate solutions but not always prove their optimality. This article discusses some conditions under which these points are in fact global or local optima.
A Symmetrical Coordinate Frame on the Hexagonal Grid for Computer Graphics and Vision
Authors: Her I.
Published: June 2008

This paper investigates the hexagonal tessellation of picture elements used in computer graphics and computer vision systems. Its purpose is to propose a symmetrical hexagonal coordinate frame to replace the existing oblique coordinate system. In the proposed symmetrical coordinate frame, spatial properties of the hexagonal grid such as distance functions are better represented.
Development of Kinematic/Kinetic Performance Tools in Synthesis of Multi-DOF Mechanisms
Authors: Lee Ming-Yih , Erdman A. G. , Gutman Y.
Published: June 2008

Kinematic and kinetic performance are important issues in designing multi-degree-of-freedom mechanisms such as robotic manipulators. In the engineering design stage, it is especially important that the designer can grasp the characteristics of the mechanism. The aim of this study is to develop a means of representing the kinematic and kinetic performance of the mechanism in such a way that the performance characteristics are quantified analytically and visible graphically to the designer in their entirety at the conceptual design stage. Various performance indices are derived from the Jacobian matrix and its quadratic form. These performance indices are the local kinematic cross-coupling index (angle of intersection between column vectors of the Jacobian), the local directional mobility index (ratio of Jacobian’s eigenvalues), and the local efficiency index (product of Jacobian’s eigenvalues). Graphical images of these performance characteristics using eigen-ellipsoid and workspace trajectory contours are introduced. Critical performance points in mechanism workspace are identified and elaborated for design considerations. Based on the graphical representation of these performance characteristics, design rules for achieving different performance objectives can easily be implemented. This method is applicable to computer-aided design of a mechanism and predetermination of its kinematic and kinetic performance.
A Null-Space Solution of the Inverse Kinematics of Redundant Manipulators Based on a Decomposition of Screws
Authors: Podhorodeski R. P. , Goldenberg A. A. , Fenton R. G.
Published: June 2008

In this paper, an approach for solving the inverse kinematics (velocity) problem for redundant open-chain manipulators is addressed. The solution is based upon finding a particular joint rate solution and identifying a joint velocity null-space basis through a decomposition of screw coordinates representing the joint axes. Optimal joint rate solutions are formulated in terms of the joint null-space basis. A specification of computational costs for numerical application is presented. The method is shown to be useful for analytical application through example derivations for two 7 revolute jointed manipulators and a platform mounted nonredundant manipulator.
A Parameterization of the Central Axis Congruence Associated with Four Positions of a Rigid Body in Space
Authors: McCarthy J. M.
Published: June 2008

Given four positions of a rigid body in space, there is a congruence of lines that can be used as the central axes of cylindric cranks to guide the body through the four positions. This “central axis congruence” is a generalization of the center point curve of planar kinematics. It is known that this congruence is identical to the screw congruence which arises in the study of complementary screw quadrilateral. It is less well-known that the screw congruence is the “screw surface” of the 4C linkage formed by the complementary screw quadrilateral, and it is this relationship that we use to obtain a parameterization for the screw congruence and in turn, the central axis congruence. This parameterization should facilitate the use of this congruence in computer based design of spatial mechanisms.
Structure of Robot Compliance
Authors: Patterson T. , Lipkin H.
Published: June 2008

The structure of nonsingular robot compliance is investigated by applying screw theory to two eigenvalue problems. For the first problem the eigenscrews are demonstrated to be Ball’s (1990) principal screws of the potential. Several new propositions are presented characterizing compliance matrix eigenstructure. Using a novel formulation, the second eigenvalue problem generalizes the three wrench-compliant axes of Dimentberg (1965) to include three twist-compliant axes. These two types of compliant axes are shown to be reciprocal and define conjugate screw systems. The wrench- and twist-compliant axes are demonstrated to the general elements of a compliant axis hierarchy.