Showing papers in "Journal of Mechanical Design in 1996"
TL;DR: This variation embodies the integration of the Response Surface Methodology (RSM) with the compromise Decision Support Problem (DSP) and is especially useful for design problems where there are no closed-form solutions and system performance is computationally expensive to evaluate.
Abstract: In this paper, we introduce a small variation to current approaches broadly called Taguchi Robust Design Methods. In these methods, there are two broad categories of problems associated with simultaneously minimizing performance variations and bringing the mean on target, namely, Type 1-minimizing variations in performance caused by variations in noise factors (uncontrollable parameters). Type II-minimizing variations in performance caused by variations in control factors (design variables). In this paper, we introduce a variation to the existing approaches to solve both types of problems. This variation embodies the integration of the Response Surface Methodology (RSM) with the compromise Decision Support Problem (DSP). Our approach is especially useful for design problems where there are no closed-form solutions and system performance is computationally expensive to evaluate. The design of a solar powered irrigation system is used as an example.
584 citations
TL;DR: In this paper, modularity of product architectures with respect to life cycle concerns, not just product functionality and structure, is defined and applied in the analysis of architecture characteristics, and a principal hypothesis underlying this work is that high degree of life cycle modularity can be beneficial across all viewpoints of interest because all interested people will view the product similarly and consistently.
Abstract: Growing concern for the environment has spurred interest in environmentally conscious design and manufacturing. The concept of Design for the Life Cycle encompasses all aspects of a product’s life cycle from initial conceptual design, through normal product use, to the eventual disposal of the product. A product’s architecture, determined during the configuration design stage, plays a large role in determining the product’s life cycle characteristics. In this paper, modularity of product architectures with respect to life cycle concerns, not just product functionality and structure, is defined and applied in the analysis of architecture characteristics. A principal hypothesis underlying this work is that high degree of life cycle modularity can be beneficial across all viewpoints of interest because all interested people will view the product similarly and consistently. An architecture decomposition algorithm from the literature is adopted for partitioning architectures into modules from each life cycle viewpoint. Two measures of modularity are proposed: one that measures module correspondence between several viewpoints, and another that measures coupling between modules. The algorithm and measures are applied to the analysis and redesign of an automotive center console. Results of applying the algorithm and measures accurately reflected our intuitive understanding of the original center console design and predicted the results of our redesign. Furthermore, these measures incorporate only configuration information of the product; hence, can be used before detailed design stages.
289 citations
TL;DR: In this paper, the pseudo-rigid-body equivalent spring stiffness is investigated and new modeling equations are proposed to model the force/deflection relationships of large-deflection members in compliant mechanisms.
Abstract: Compliant mechanisms gain some or all of their mobility from the flexibility of their members rather than from rigid-body joints only. More efficient and usable analysis and design techniques are needed before the advantages of compliant mechanisms can be fully utilized. In an earlier work, a pseudo-rigid-body model concept, corresponding to an end-loaded geometrically nonlinear, large-deflection beam, was developed to help fulfill this need. In this paper, the pseudo-rigid-body equivalent spring stiffness is investigated and new modeling equations are proposed. The result is a simplified method of modeling the force/deflection relationships of large-deflection members in compliant mechanisms. The resulting models are valuable in the visualization of the motion of large-deflection systems, as well as the quick and efficient evaluation and optimization of compliant mechanism designs.
255 citations
Journal Article•
TL;DR: In this paper, an N-2-1 locating principle has been proposed and verified to be valid for deformable sheet metal parts as compared to the widely accepted 3 2 1 principle for rigid bodies.
Abstract: Fixture design is an important consideration in all manufacturing operations. Central to this design is selecting and positioning the locating points. While substantial literature exists in this area, most of it is for prismatic or solid workpieces. This paper deals with sheet metal fixture design. An ''N-2-1'' locating principle has been proposed and verified to be valid for deformable sheet metal parts as compared to the widely accepted 3-2-1 principle for rigid bodies. Based on the N-2-1 principle, algorithms for optimal fixture design are presented using finite element analysis and nonlinear programming methods to find the best N locating points such that total deformation of the deformable sheet metal is minimized. A simulation package called OFixDesign is introduced and numerical examples are presented to validate the N-2-1 principle and optimal sheet metal fixture design approach.
234 citations
TL;DR: The pseudo-rigid-body-model concept is used to develop a loop-closure method for the analysis and synthesis of compliant mechanisms that allows compliant mechanisms to be designed for tasks that would have earlier been assumed to be unlikely, if not impossible, applications of compliant mechanism.
Abstract: Compliant mechanisms gain at least some of their motion from flexible members. The combination of large-deflection beam analysis, kinematic motion analysis, and energy storage makes the analysis of compliant mechanisms difficult. The design of mechanisms often requires iteration between synthesis and analysis procedures. In general, the difficulty in analysis has limited the use of compliant mechanisms to applications where only simple functions and motions are required. The pseudo-rigid-body model concept promises to be the key to unifying the compliant and rigid-body mechanism theories. It simplifies compliant mechanism analysis by determining an equivalent rigid-body mechanism that accurately models the kinematic characteristics of a compliant mechanism. Once this model is obtained, many well known concepts from rigid-body mechanism theory become amenable for use to analyze and design compliant mechanisms. The pseudo-rigid-body-model concept is used to develop a loop-closure method for the analysis and synthesis of compliant mechanisms. The method allows compliant mechanisms to be designed for tasks that would have earlier been assumed to be unlikely, if not impossible, applications of compliant mechanisms.
213 citations
TL;DR: A taxonomy of elemental mechanical functions which can be used with many decomposition techniques is presented, used as a pedagogical tool or as a basis for the derivation of a complete taxonomy.
Abstract: As design methods are studied, the usefulness of function-based methodologies becomes clear. However, for these methodologies to be fully utilized, there must be some standardization of the functions used to provide a common language. This paper presents a taxonomy of elemental mechanical functions which can be used with many decomposition techniques. The taxonomy can be used as a pedagogical tool or as a basis for the derivation of a complete taxonomy. Also discussed are generic forms and how they interact with the taxonomy.
185 citations
TL;DR: In this paper, the authors developed a continuation method that accounts for simple and multiple bifurcation of one-dimensional solution curves and derived second order Taylor expansions for finding tangents to solution curves at simple bifurlcation points of continuation equations and characterizing barriers to control of manipulators.
Abstract: Numerical algorithms for mapping boundaries of manipulator workspaces are developed and illustrated. Analytical criteria for boundaries of workspaces for both manipulators having the same number of input and output coordinates and redundantly controlled manipulators with a larger number of inputs than outputs are well known, but reliable numerical methods for mapping them have not been presented. In this paper, a numerical method is first developed for finding an initial point on the boundary. From this point, a continuation method that accounts for simple and multiple bifurcation of one-dimensional solution curves is developed. Second order Taylor expansions are derived for finding tangents to solution curves at simple bifurcation points of continuation equations and for characterizing barriers to control of manipulators. A recently developed method for tangent calculation at multiple bifurcation points is employed. A planar redundantly controlled serial manipulator is analyzed, determining both the exterior boundary of the accessible output set and interior curves that represent local impediments to motion control. Using these methods, more complex planar and spatial Stewart platform manipulators are analyzed in a companion paper.
131 citations
TL;DR: In this article, an extended three-dimensional model is used for calculating dynamic tooth loads on a planetary gear set and an original Ritz method aimed at solving large parametrically excited differential systems is proposed.
Abstract: An extended three-dimensional model is used for calculating dynamic tooth loads on a planetary gear set. Time dependent mesh stiffnesses are determined and an original Ritz method aimed at solving large parametrically excited differential systems is proposed. Results from the Ritz method compare favorably with those given by direct integrations for highly reduced computation times. The difference between local critical speeds (for one individual mesh) and global critical speeds (for sun or ring gear-planet meshes) on a sequential spur gear train is pointed out. Finally, it is shown that, for linear behaviors, mesh stiffnesses are largely controlling dynamic tooth loads while the influence of a floating sun or ring gear is less important.
130 citations
TL;DR: The basic theory of rational motions is summarized and a linear control structure for piecewise rational motions suitable for geometry processing is introduced and algorithms for the calculation of the surface which is swept out by a moving polyhedron are provided.
Abstract: Using rational motions it is possible to apply many fundamental B-spline techniques to the design of motions. The present paper summarizes the basic theory of rational motions and introduces a linear control structure for piecewise rational motions suitable for geometry processing. Moreover it provides algorithms for the calculation of the surface which is swept out by a moving polyhedron and examines interpolation techniques. The methods presented in this paper can be applied to various problems in computer animation as well as in robotics.
117 citations
TL;DR: In this paper, the effects of deformation on component tolerances using linear mechanics were evaluated for two basic configurations, assembly in series and assembly in parallel, using analytical methods and multiple joints beyond the basic configurations were further examined using numerical methods.
Abstract: Traditional tolerance analyses such as the worst case methods and the statistical methods are applicable to rigid body assemblies. However, for flexible sheet metal assemblies, the traditional methods are not adequate: the components can deform, changing the dimensions during assembly. This paper evaluates the effects of deformation on component tolerances using linear mechanics. Two basic configurations, assembly in series and assembly in parallel, are investigated using analytical methods. Assembly sequences and multiple joints beyond the basic configurations are further examined using numerical methods (with finite element analysis). These findings constitute a new methodology for the tolerancing of deformable parts.
115 citations
TL;DR: This article compares the genetic-algorithm-based technique with homogenization methods in the minimization of a structure’s compliance subject to a maximum volume constraint and uses the technique to generate topologies combining high structural performance with a variety of material connectivity characteristics which arise directly from the discretized design representation.
Abstract: The genetic algorithm (GA), an optimization technique based on the theory of natural selection, is applied to structural topology design problems. After reviewing the genetic algorithm and previous research in structural topology optimization, we detail the chromosome-to-design representation which enables the genetic algorithm to perform structural topology optimization. Extending our prior investigations, this article first compares our genetic-algorithm-based technique with homogenization methods in the minimization of a structure’s compliance subject to a maximum volume constraint. We then use our technique to generate topologies combining high structural performance with a variety of material connectivity characteristics which arise directly from our discretized design representation. After discussing our findings, we describe potential future work.
TL;DR: In this article, it is shown that the objective of design optimization as defined by the customers via contemporary approaches can lead the designer to highly inappropriate and undesirable designs, and it becomes apparent that the methods of TQM and QFD can lead to highly erroneous results.
Abstract: Many modem approaches to engineering design seek to optimize design in order to maximize the value of the system to its customers. These approaches rely on the formulation of a system utility function as a measure of system worth. It is shown here that, under certain circumstances, however, such a measure cannot exist. It is then indicated that these circumstances comprise the rule rather than the exception. Finally it is shown that pursuing the objective of design optimization as defined by the customers via contemporary approaches can lead the designer to highly inappropriate and undesirable designs. As a consequence of this, it becomes apparent that the methods of Total Quality Management (TQM) and Quality Function Deployment (QFD) can lead to highly erroneous results.
TL;DR: In this paper, a unified slip theory is presented for flat belts, V-belts and V-ribbed belts considering creep, shear, seating/unseating and compliance.
Abstract: Slip measurements on thick flat belts, V-belts and V-ribbed belts running on small pulleys reveal that the slip is much higher than can be predicted with classical creep theory. Shear creep plays an important role and special care must be taken when analyzing the shear deflection of the V-belt and the ribs of the V-ribbed belt. Other mechanisms are present as well. The behavior in the seating and unseating regions changes the direction of the frictional forces in these regions on the driver pulley. A unified slip theory is presented for flat belts, V-belts and V-ribbed belts considering creep, shear, seating/unseating and compliance. Measurements and theory fit very well for practical tension levels. At low tension the measured slip is higher than the predicted one for V-belts and V-ribbed belts, which probably depends on the poor fit between the belt and the grooved pulley.
TL;DR: In this paper, an analytical expression of the time-varying contact length between perfect involute spur and helical gears is presented, whose numerical expansions correlate well with the results of numerical time-step simulations based on contact length discretization.
Abstract: This paper presents an analytical expression of the time-varying contact length between perfect involute spur and helical gears. It is shown that contact lengths can be expressed as Fourier series whose numerical expansions correlate very well with the results of numerical time-step simulations based on contact length discretization. Finally, some possible examples of application in gear dynamics are suggested.
TL;DR: In this paper, a loaded gear drive with point contact between tooth surfaces is considered and the principal curvatures and directions at a current point of tangency, the contact paths on tooth surfaces, and the transmission errors caused by misalignment are considered as known.
Abstract: A loaded gear drive with point contact between tooth surfaces is considered. The principal curvatures and directions at a current point of tangency, the contact paths on tooth surfaces, and the transmission errors caused by misalignment we consider as known. In this paper the following topics are covered: (1) Determination of the contact force and its distribution over the contact ellipse; (2) Determination of the tooth deflection, the load share, and the real contact ratio; and (3) Stress analysis by application of the finite element method. The discussed approach is illustrated with a numerical example.
TL;DR: These metrics for assessing the design freedom and information certainty associated with a ranged set of top-level design specifications are applied to an example problem, namely, the conceptual design of a family of aircraft.
Abstract: Our primary focus in this paper is on open engineering systems which are readily adaptable to changing design requirements Designing an open engineering system allows a family of products to be developed around a common baseline model This entails increasing design freedom and design knowledge during the early stages of design Toward this end, developing ranged sets (as opposed to points sets) of top-level design specifications provides a means to improve system flexibility by increasing design knowledge while maintaining design freedom Consequently, our secondary focus in this paper is on metrics for assessing the design freedom and information certainty associated with a ranged set of top-level design specifications As a demonstration, these metrics are applied to an example problem, namely, the conceptual design of a family of aircraft Our emphasis in this paper is on introducing open engineering systems and metrics for design freedom and information certainty, not on our example, per se
TL;DR: In this paper, the sensitivity Jacobian is used to determine the sensitivity of tolerances to the performance quality of mechanisms and a technique to identify a robust design, which is the least sensitive to the tolerances.
Abstract: This paper presents a general theory to determine the sensitivity of tolerances to the performance quality of mechanisms and a technique to identify a robust design, which is the least sensitive to the tolerances. The method is demonstrated in position synthesis of linkages. The sensitivity Jacobian is first introduced to relate the performance tolerances and the dimensional tolerances. The Rayleigh quotient of the sensitivity Jacobian, which is equivalent to Taguchi's signal to noise ratio, is then used to define the performance quality and a sensitivity index is introduced to measure the sensitivity of the performance quality to the dimensional tolerances for the whole system. The ideal tolerance distribution is obtained in closed form. It shows how the tolerance specification affects the performance quality and that the performance quality can be significantly improved by tightening a key tolerance while loosening the others. The theory is general and the technique can be adapted easily for other mechanical systems, including multiple-loop linkages.
TL;DR: In this article, a displacement analysis of actively articulated wheeled vehicles on uneven terrain is presented, where the displacement analysis leads to multiple solutions due to the inherent nonlinearity in the position kinematic equations.
Abstract: This manuscript presents a displacement analysis of actively articulated wheeled vehicles on uneven terrain. These vehicles are distinct from traditional wheeled systems since they have the ability to actively adapt to variations in the terrain and they can actively influence the forces at the wheel-terrain contact locations. They also possess special mobility capabilities such as obstacle climbing and self-recovery from an over-turn failure. The problem of solving for the configuration of these vehicles on uneven terrain has been addressed in detail. The displacement analysis leads to multiple solutions due to the inherent nonlinearity in the position kinematic equations. Geometric reasoning has been used to identify the particular configuration that represents the correct vehicle geometry on the terrain. Apllications of the displacement analysis algorithms to vehicle planning on uneven terrain have been discussed. An obstacle climbing maneuver of a three-module actively articulated wheeled vehicle has been described.
TL;DR: In this paper, the effects of damping on rotational vibratory solutions of a multiple pulley-flat viscoelastomeric belt system with rotary arm tensioner are developed.
Abstract: The effects of damping on rotational vibratory solutions of a multiple pulley-flat viscoelastomeric belt system with rotary arm tensioner is developed. A complex model procedure is developed to solve both underdamped and overdamped cases. This complex modal procedure allows for future extension to include nonsymmetric rotational models, such as transverse belt vibration coupling. The modal solution enables rapid analysis over a spectrum of frequencies. Seven pulley system experimental results reported in the literature support the analytical development. Belt damping has significant vibration and belt tension amplitude effects. Tensioner spring rate and coulomb damping has minor effects.
TL;DR: In this paper, the authors presented a computer simulation showing how the gear contact ratio affects the dynamic load on a spur gear transmission, and found that the contact ratio can be affected by the tooth addendum, the pressure angle, the tooth size, and the center distance.
Abstract: This paper presents a computer simulation showing how the gear contact ratio affects the dynamic load on a spur gear transmission. The contact ratio can be affected by the tooth addendum, the pressure angle, the tooth size (diametral pitch), and the center distance. The analysis presented in this paper was performed by using the NASA gear dynamics code DANST. In the analysis, the contact ratio was varied over the range 1.20 to 2.40 by changing the length of the tooth addendum. In order to simplify the analysis, other parameters related to contact ratio were held constant. The contact ratio was found to have a significant influence on gear dynamics. Over a wide range of operating speeds, a contact ratio close to 2.0 minimized dynamic load. For low-contact-ratio gears (contact ratio less than two), increasing the contact ratio reduced gear dynamic load. For high-contact-ratio gears (contact ratio equal to or greater than 2.0), the selection of contact ratio should take into consideration the intended operating speeds. In general, high-contact-ratio gears minimized dynamic load better than low-contact-ratio gears.
TL;DR: In this article, the usefulness of including likely separation techniques in early design for recycling guidelines is discussed, and a simple method for determining the appropriate separation process in the early stages of design is presented.
Abstract: Virtually all of the material in today’s automobiles can technically be recycled. The challenge facing engineers is making this recycling process economical, especially for materials in such components as seats and instrument panels. Recycling these components requires the different materials to be separated so that each can be recycled individually. This separation can be accomplished either manually, where workers disassembly and sort the vehicle components by hand, or mechanically, where the vehicle is shredded and the materials sorted by properties such as conductivity and density. In this paper, the usefulness of including likely separation techniques in DFR guidelines is discussed. Three vehicles were dismantled at the VRDC as part of an effort to establish a baseline of current vehicle recyclability. Concurrently, this allowed examination of the effectiveness of the early design for recycling (DFR) efforts. The applicability of common design guidelines to the two types of separation is discussed, and a simple method for determining the appropriate separation process in the early stages of design is presented.
TL;DR: Working capability analysis of planar and spatial Stewart platforms with unilateral constraints on actuator length is carried out using numerical methods based on analytical criteria for the boundary of the accessible output set to be characterized by a family of one dimensional generators.
Abstract: Working capability analysis of planar and spatial Stewart platforms with unilateral constraints on actuator length is carried out using numerical methods based on analytical criteria for the boundary of the accessible output set. Restrictions on achievable motion at singular configurations associated with points interior to the accessible output set are also analyzed. Since movement of the working point on a spatial Stewart platform occurs in three-dimensional space, the boundary of the accessible output set is a two-dimensional surface. Numerical methods used in this analysis map one-dimensional solution sets, permitting the boundary of the accessible output set to be characterized by a family of one dimensional generators. Motion control restrictions inside the accessible output set are similarly characterized by families of interior singular curves, and barriers to motion control across surfaces defined are analyzed.
TL;DR: The objective of this paper is to provide an efficient and reliable method for computing the shortest path between two points on a free-form parametric surface and the shortest approach to solving the two point boundary value problem.
Abstract: Computation of shortest paths on free-form surfaces is an important problem in ship design, robot motion planning, computation of medial axis transforms of trimmed surface patches, terrain navigation and NC machining. The objective of this paper is to provide an efficient and reliable method for computing the shortest path between two points on a free-form parametric surface and the shortest path between a point and a curve on a free-form parametric surface. These problems can be reduced to solving a two point boundary value problem. Our approach for solving the two point boundary value problem is based on a relaxation method relying on finite difference discretization. Examples illustrate our method.
TL;DR: In this paper, the shape and topology of a structural component are optimized with the objective of minimizing the compliance subject to a constraint on the total mass of the structure, which is defined as the boundary of the shape.
Abstract: In this paper, a method is proposed for the design optimization of structural components where both shape and topology are optimized. The boundaries of the shape of the structure are represented using contours of a shape density function. The contour of the density function corresponding to a threshold value is defined as the boundary of the shape. The shape density function is defined over a feasible domain and is represented by a continuous piece-wise interpolation over the finite elements used for structural analysis. The values of the density function at the nodes serve as the design variables of the optimization problem. The advantage of this shape representation is that both shape and topology of the structure can be modified and optimized by the optimization algorithm. Unlike previous methods for shape and topology optimization, the material is not modeled as porous or composite using the homogenization method. Instead the material properties of the structure are assumed to depend on the density function and many approximate material property-density relations have been studied. The shape and topology of structural components are optimized with the objective of minimizing the compliance subject to a constraint on the total mass of the structure.
TL;DR: In this article, a geometric construction that maps a space curve onto a surface curve is presented, which is designed to be coordinate independent and provides isoparametric maps for multiple surface curves.
Abstract: A novel technique for designing curves on surfaces is presented. The design specifications for this technique derive from other works on curvature continuous surface fairing. Briefly stated, the technique must provide a computationally efficient method for the design of surface curves that is applicable to a very general class of surface formulations. It must also provide means to define a smooth natural map relating two or more surface curves. The resulting technique is formulated as a geometric construction that maps a space curve onto a surface curve. It is designed to be coordinate independent and provides isoparametric maps for multiple surface curves. Generality ofthe formulation is attained by solving a tensorial differential equation formulated in terms of local differential properties of the surfaces. For an implicit surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This technique has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations.
TL;DR: In this article, the authors present an alternative approach by varying the speed of the cam to reduce the peak values of the follower output motion characteristics, which can be used to select suitable cam speed trajectories.
Abstract: A cam is often assumed to be operated at a constant speed in designing a cam-follower system. The motion characteristics of the follower are determined once the cam displacement curve is designed. The traditional design method for improving the motion characteristics is to find a new displacement curve which has better motion characteristics. This paper, however, presents an alternative approach by varying the speed of the cam to reduce the peak values of the follower output motion characteristics. Constraints and design criteria for selecting suitable cam speed trajectories are then developed. Finally, examples are given to illustrate the design procedure and also to show its feasibility.
TL;DR: In this paper, a method was presented to minimize the static transmission error using cubic splines (C.S.) for gear tooth profile, which is expected to reduce the gear vibration and noise by lowering the dynamic tooth load in a meshing cycle.
Abstract: A novel method was presented by the authors to minimize the static transmission error using cubic splines (C.S.) for gear tooth profile. A reduction in the transmission error is expected to reduce the gear vibration and noise by lowering the dynamic tooth load in a meshing cycle. To establish this fact, a dynamic analysis of the gear drive with involute tooth and modified tooth profiles (using C.S.) is performed. For this, first the tooth deformation is found and then the tooth dynamic load is determined for all reasonable speeds. A parametric study is conducted to establish the superiority of the C.S. based gear profile over the involute profile as well as the other profiles based on the use of linear and parabolic tip reliefs.
TL;DR: In this paper, a methodology based on the geometry of the injection molded part to identify the draw direction range and parting line locations is presented, which is a function of the interaction of the outward normals of the surfaces that have been divided into concave and convex regions of the part.
Abstract: This paper presents a methodology based on the geometry of the injection molded part to identify the draw direction range and parting line locations. These parameters are shown to be a function of the interaction of the outward normals of the surfaces that have been divided into concave and convex regions of the part. This approach can also be applied incrementally to determine these mold parameters for a part as design features are added. The designer can then select from the choices provided to find the optimum parting line location and draw direction using heuristic rules. An absence of an allowable draw direction indicates the presence of an undercut that complicates the mold by requiring a side action so that the mold cost increases. The designer can either redesign the part or accept the undercut by specifying a side core or cavity. Design examples are provided which illustrate the effectiveness of the developed approach.
TL;DR: In this article, the authors describe the set of all singular configurations of serial robot-manipulators and give an algorithm to determine the degree of a singularity from the knowledge of the actual configuration of axes of the robot.
Abstract: This paper is devoted to the description of the set of all singular configurations of serial robot-manipulators. For 6 degrees of freedom serial robot-manipulators we have developed a theory which allows to describe higher order singularities. By using Lie algebra properties of the screw space we give an algorithm, which determines the degree of a singularity from the knowledge of the actual configuration of axes of the robot-manipulator only. The local shape of the singular set in a neighbourhood of a singular configuration can be determined as well. We also solve the problem of escapement from a singular configuration. For serial robot-manipulators with the number of degrees of freedom different from six we show that up to certain exceptions singular configurations can be avoided by a small change of the motion of the end-effector. We also give an algorithm which allows to determine equations of the singular set for any serial robot-manipulator. We discuss some special cases and give examples of singular sets including PUMA 560.
TL;DR: In this paper, a closed-form resolution scheme of the forward kinematics of parallel manipulators based on two concepts, local structurization and mechanism partition, is presented. But it is not shown that one extra sensor is sufficient for both 3-3 and 6-3 SPM, and two sensors for 6-6 SPM.
Abstract: This paper presents a new closed-form resolution scheme of the forward kinematics of parallel manipulators based on two concepts, local structurization and mechanism partition. This scheme is applied to 6-DOF Stewart platform manipulators and the effectiveness of this scheme is verified through numerical examples. It is shown that one extra sensor is sufficient for both 3-3 SPM and 6-3 SPM to exactly resolve the forward kinematic problem (FKP) in closed form and two sensors for 6-6 SPM. In previous research, at least three extra sensors were needed for closed-form resolution of the FKP for 6-6 SPM. Consequently, the new resolution scheme is efficient to implement and easy for real-time applications for the control of parallel manipulators.