A Virtual Reality Environment for Synthesizing Spherical Four-bar Mechanisms

This paper describes the development of a virtual reality environment which facilitates the design of spherical four-bar mechanisms. A short discussion of spherical mechanism design theory and computer-aided mechanism design is followed by a description of the virtual environment and the development and operation of the SphereVR program. The virtual environment allows the user to naturally interact with the input data and specify the design parameters while operating in a three-dimensional environment. We see this development as a logical extension of existing graphics-based spatial design software. The need for a three-dimensional design space is driven by the difficulty in specifying design inputs and constraints for a spatial problem using a two-dimensional interface. In addition, once the mechanism has been created, the virtual environment provides the opportunity for the user to visually verify that the mechanism will perform the desired three-dimensional motion

Spherical Mechanism Synthesis in Virtual Reality

This paper presents a new approach to using virtual reality (VR) to design spherical mechanisms. VR provides a three dimensional design space where a designer can input design positions using a combination of hand gestures and motions and view the resultant mechanism in stereo using natural head movement to change the viewpoint. Because of the three dimensional nature of the design and verification of spherical mechanisms, VR is examined as a new design interface in this research. In addition to providing a VR environment for design, the research presented in this paper has focused on developing a “design in context” approach to spherical mechanism design. Previous design methods have involved placing coordinate frames along the surface of a constraint sphere. The new “design in context” approach allows a designer to freely place geometric models of movable objects inside an environment consisting of fixed objects. The fixed objects could either act as a base for a mechanism or be potential sources of interference with the motion of the mechanism. This approach allows a designer to perform kinematic synthesis of a mechanism while giving consideration to the interaction of that mechanism with its application environment

High-Order Dimension Synthesis of Planar/Spatial Mechanisms with One-DoF by CAD Variational Geometry

This paper proposes a (computer aided design) CAD variational geometry approach for the high-order dimension synthesis of one-DoF mechanisms based on the given velocity/acceleration of a moving platform along a prescribed trajectory. The objective of this approach is to determine the reasonable dimensions of the mechanisms when given the velocity or/and the acceleration of the moving platform along a prescribed trajectory. First, some concepts and mathematical foundations are explained for constructing the velocity/acceleration simulation mechanism of a general mechanism. Second, the inverse velocity/acceleration simulation mechanisms of the planar/spatial four-bar mechanisms with one-DoF are constructed by the CAD variational geometry. Third, when given the position and the velocity/acceleration of the coupler along a prescribed trajectory, all the reasonable dimensions of the planar/spatial four-bar mechanisms are solved from their simulation mechanisms

Kinematic synthesis of adjustable spatial four and five-bar mechanisms for finite and multiply separated positions

Although spatial mechanisms are more general in structure than planar mechanisms, their applications are few due to the limited number of practical design tools and the complexity of those available. It is in fact the task of the future to develop effective, but practical design tools for spatial mechanisms. This research presents several new methods for synthesizing adjustable spatial mechanisms. The first method involves the kinematic synthesis of spatial mechanisms for multiphase motion generation. Using this method, spatial four and five-bar mechanisms can be synthesized to achieve different phases of prescribed rigid body positions. The theory of this approach has also been extended to incorporate rigid body tolerance problems. Using the tolerance problem method, spatial four-bar mechanisms can be synthesized to achieve the prescribed precise rigid body positions and also satisfy the rigid body positions within the prescribed tolerances. Both approaches use the R-R, S-S, R-S and C-S dyad displacement equations. The second method involves the kinematic synthesis of spatial mechanisms for multiphase multiply separated positions. Using this method, spatial four and five-bar mechanisms can be synthesized to achieve different phases of prescribed rigid body positions, velocities and accelerations. The theory of this approach has also been extended to incorporate instantaneous screw axis (ISA) parameters. Using ISA parameters, spatial four-bar mechanisms can also be synthesized to achieve different phases of prescribed rigid body positions, velocities and accelerations. Both approaches use the R-R, S-S, R-S and C-S dyad displacement, velocity and acceleration equations. For each method, the maximum number of prescribed rigid positions is determined for each mechanism for two and three phase problems. The spatial four and five-bar mechanisms considered in this research are the RRSS, RRSC, RSSR-SS and RSSR-SC

기구 위상 및 치수 통합 합성 기법 개발과 이를 응용한 차량 현가 장치 개념설계

학위논문 (박사)-- 서울대학교 대학원 공과대학 기계항공공학부, 2017. 8. 김윤영.Topology optimization of rigid-link mechanisms, a methodology for obtaining linkages that satisfy a set of user defined kinematic requirements without any a priori baseline design, is a new paradigm that can be usefully employed in industries such as automotive or aerospace engineering. In previous research, however, the methodology has been limited to simple planar linkages. In this research, a new formulation for synthesizing the topology and dimension of linkages is proposed. To design topology of link mechanisms by using the optimization method, a formulation which represents the DOF (Degree-of-Freedom) in differentiable form has to be considered. Herein, the DOF is the minimum number of actuators that is required to decide the position of the all link components. In previous research, motion compliance and load stiffness have been employed to avoid deficient-DOF state and redundant-DOF state, respectively. To this end, the motion compliance is the system flexibility under displacement excitation such as motion drive, and the load stiffness is the system rigidity under force excitation such as external resistance forces. However, in aspect of the multi-objective optimization, implementation of the DOF control by using the two functions, the motion compliance and load stiffness, contradictive to each other is quite particular about heuristic weighting factor decision issue. Meanwhile, as the work transmittance efficiency function suggested in this thesis is exploited to control the system DOF, there is no issue related to the preference decision between two objective functions. That is, only a unified objective function is used to avoid the deficient- and the redundant-DOF states. Therefore, it is possible to design complicated systems, unlike the previous research which is hard to consider it due to difficulties of the DOF control. Our approach is validated through several case studies. In the planar design case, benchmark type four-bar linkages and automotive steering systems are considered. For spatial linkage synthesis problems, automotive suspension mechanisms are designed by the suggested method. To find a better solution in suspension design, we employed a simultaneous topology and shape optimization method. As a result, a new type suspension mechanism is obtained by the unified topology and dimension synthesis method, especially when a smaller design space compared with nominal one is provided. To analyze the behavior of the newly designed suspension system, the screw-axis theory is applied. From this investigation, it is found that a new special module is included in the new-concept suspension and it works as a conventional link component. In this research, according to this property of the newly proposed concept, it will be called a hidden link suspension. It is also shown that the suspension installation space can be reduced compared with nominal multi-link type suspensions by exploiting the hidden link module. The synthesized suspension mechanism is the first successful industrial result obtained by the unified topology and dimension synthesis method. Especially, the proposed method can provide new insight to engineers who want to enhance the product quality by making use of totally different conceptual designs as shown in this research. In the near future, it will be possible to apply the suggested linkage synthesis method to other practical problems, beyond the automotive industry problems, to find more advanced mechanisms.1. INTRODUCTION 1 1.1 Motivation: review of conventional synthesis methods 3 1.2 Previous researches for unified synthesis of mechanisms 10 1.3 Main contributions of this thesis 20 2. TOPOLOGY OPTIMIZATION METHOD FOR LINKAGE MECHANISMS 25 2.1 Definition of problem 27 2.2 Modeling, analysis, and formulation 32 2.2.1 Modeling and Analysis 32 2.2.2 Objective function 37 2.3 Mechanism synthesis by the proposed formulation 46 2.3.1 Synthesis of Grashof-type four-bar linkage mechanisms 46 2.3.2 Synthesis of steering linkage mechanisms 50 2.4 Post-processing 56 2.4.1 Step 1: Binarizing 56 2.4.2 Step 2: Pruning 56 2.4.3 Step 3: Simplification 57 2.5 Summary 62 3. SPATIAL VEHICLE SUSPENSION DESIGN BY USING SIMULTANEOUS TOPOLOGY AND SHAPE OPTIMIZATION 85 3.1 Review of recently developed suspension design methods 87 3.2 Ground structure model and kinematic analysis 90 3.2.1 Spatial ground structure composed of bars and springs 90 3.2.2 Nonlinear finite element analysis of spatial bar elements 92 3.2.3 Rigid-body motion and constraint of the hub-carrier 97 3.2.4 Governing equations for kinematic analysis 101 3.3 Optimization based formulation for mechanism synthesis 104 3.3.1 Design variables and interpolation 104 3.3.2 Work transmittance efficiency based formulation 106 3.3.3 Design sensitivity analysis for design optimization 112 3.4 Suspension mechanism synthesis by the proposed method 114 3.4.1 Recovery of double wishbone and multilink suspensions 114 3.4.2 Synthesis of suspensions satisfying R&H requirements 119 3.4.3 Interpretation of the optimized suspension layouts 126 3.5 Summary 132 4. NEW CONCEPT SUSPENSION INCLUDING HIDDEN LINK MODULE 145 4.1 Overview 145 4.2 A new concept obtained from topology optimization 147 4.2.1 A special module included in the new concept 147 4.2.2 Strategy for interpretation of the special module 149 4.3 Force transmission analysis 152 4.3.1 Introduction of the screw axis theory 153 4.3.2 Force transmission analysis of the RSR-limb 159 4.3.3 Suggestion of hidden link concept 164 4.3.4 Validation of the hidden link concept 166 4.4 Nonlinear effects of the hidden link suspension 174 4.4.1 Effective length of the hidden link in nonlinear motion 176 4.4.2 Prediction of the effective length of the hidden link 181 4.4.3 Design guide line of the hidden link suspension 186 4.5 Summary 192 5. CONCLUSIONS 211 APPENDIX A REMEDIES FOR THE MESH DEPENDENCY ISSUE 216 A.1 Overview 216 A.2 Coarse-to-fine mesh converting approach 218 A.3 Simultaneous topology and shape optimization approach 222 APPENDIX B WRENCH SCREW ANALYSIS 231 B.1 Overview 231 B.2 Wrench screw of arm component 232 B.3 Wrench screw of RSR limb module 237 APPENDIX C VIRTUAL PRODUCT DEVELOPMENT FOR VALIDATION OF HIDDEN LINK CONCEPT 242 C.1 Overview 242 C.2 Virtual Product development process 243 REFERENCES 248 ABSTRACT (KOREAN) 259 ACKNOWLEDGEMENTS 262Docto

Biokinematic analysis of human body

Thesis (Doctoral)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2011Includes bibliographical references (leaves: 118-123)Text in English; Abstract: Turkish and Englishxiii, 123 leavesThis thesis concentrates on the development of rigid body geometries by using method of intersections, where simple geometric shapes representing revolute (R) and prismatic (P) joint motions are intersected by means of desired space or subspace requirements to create specific rigid body geometries in predefined octahedral fixed frame. Using the methodical approach, space and subspace motions are clearly visualized by the help of resulting geometrical entities that have physical constraints with respect to the fixed working volume. Also, this work focuses on one of the main areas of the fundamental mechanism and machine science, which is the structural synthesis of robot manipulators by inserting recurrent screws into the theory. After the transformation unit screw equations are presented, physical representations and kinematic representations of kinematic pairs with recurrent screws are given and the new universal mobility formulations for mechanisms and manipulators are introduced. Moreover the study deals with the synthesis of mechanisms by using quaternion and dual quaternion algebra to derive the objective function. Three different methods as interpolation approximation, least squares approximation and Chebyshev approximation is introduced in the function generation synthesis procedures of spherical four bar mechanism in six precision points. Separate examples are given for each section and the results are tabulated. Comparisons between the methods are also given. As an application part of the thesis, the most important elements of the human body and skeletal system is investigated by means of their kinematic structures and degrees of freedom. At the end of each section, an example is given as a mechanism or manipulator that can represent the behavior of the related element in the human body

Design and Prototyping of a Shape-changing Rigid-body Human Foot in Gait

Traditional ankle-foot prostheses often replicate the physiological change in shape of the foot during gait via compliant mechanisms. In comparison, rigid-body feet tend to be simplistic and largely incapable of accurately representing the geometry of the human foot. Multi-segment rigid-body devices offer certain advantages over compliant mechanisms which may be desirable in the design of ankle-foot devices, including the ability to withstand greater loading, the ability to achieve more drastic shape-change, and the ability to be synthesized from their kinematics, allowing for realistic functionality without prior accounting of the complex internal kinetics of the foot. This work focuses on applying methodology of shape-changing kinematic synthesis to design and prototype a multi-segment rigid-body foot device capable of matching the dynamic change in shape of a human foot in gait. Included are discussions of an actuation strategy, mechanical design considerations, limitations, and potential prosthetic design implications of such a foot

Structural and kinematic synthesis of overconstrained mechanisms

Thesis (Doctoral)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2012Includes bibliographical references (leaves: 133-140)Text in English; Abstract: Turkish and Englishxiii, 140 leavesInvestigation on overconstrained mechanisms needs attention especially in the structural synthesis. Knowing overconstrained conditions and including them in the design process will help creating manipulators with less degree of freedom (DoF) and more rigidity. Also this knowledge of overconstrained conditions will clarify concept of mobility of the parallel manipulators. Another subject, kinematic synthesis of overconstrained mechanisms, is important because it will allow describing a function, path, or motion with less DoF less number of joints. The aim of this thesis is to describe a generalized approach for structural synthesis and creation of new overconstrained manipulators and to describe a potentially generalizable approach for function and motion generation synthesis of overconstrained mechanism. Moreover, screw theory is investigated as a mathematical base for defining kinematics of overconstrained mechanisms. Also, overconstrained mechanisms are investigated and generation of new mechanisms is introduced with examples. Some mathematical models for the subspace geometries are given. A method for defining overconstrained simple structural groups is introduced and extended to design of manipulators with examples and solid drawings. Linear approximation and least squares approximation methods are used for the function generation and motion generation of overconstrained 6R mechanisms. A gap of describing overconstrained manipulators is filled in the area of structural synthesis. A general methodology is described for structural synthesis, mobility and motion calculations of overconstrained manipulators using simple structural groups. A potentially generalizable method for the kinematic synthesis of overconstrained manipulators is described both for function and motion generation

Design and implementation of an actively adjustable spring mechanism via redundant actuation

This study presents the theoretical results and experimental validation of an adjustable stiffness mechanism. The use of redundant actuation is emphasized in the design of a one-degree-of-freedom Watt II mechanism capable of independently controlling the effective stiffness without a change in equilibrium position. This approach is in contrast to previous spring mechanism designs unable to actively control the spring rate independent of deflection, and has potential applications in various types of suspension and assembly systems. Results indicate that driving the redundantly actuated, unidirectional, spring mechanism requires attaching two direct brush-type direct current motors on each of the two grounded revolute joints, and that the concept of adjustable springs has proven to be valid regardless of the friction effects. The torques are controlled with corresponding power amplifiers which incorporate current control loops, and the effective stiffness of the system is dependent on the redundant actuator torques of the motors

Distance-based formulations for the position analysis of kinematic chains

This thesis addresses the kinematic analysis of mechanisms, in particular, the position analysis of kinematic chains, or linkages, that is, mechanisms with rigid bodies (links) interconnected by kinematic pairs (joints). This problem, of completely geometrical nature, consists in finding the feasible assembly modes that a kinematic chain can adopt. An assembly mode is a possible relative transformation between the links of a kinematic chain. When an assignment of positions and orientations is made for all links with respect to a given reference frame, an assembly mode is called a configuration. The methods reported in the literature for solving the position analysis of kinematic chains can be classified as graphical, analytical, or numerical. The graphical approaches are mostly geometrical and designed to solve particular problems. The analytical and numerical methods deal, in general, with kinematic chains of any topology and translate the original geometric problem into a system of kinematic analysis of all the Assur kinematic chains resulting from replacing some of its revolute joints by slider joints. Thus, it is concluded that the polynomials of all fully-parallel planar robots can be derived directly from that of the widely known 3-RPR robot. In addition to these results, this thesis also presents an efficient procedure, based on distance and oriented area constraints, and geometrical arguments, to trace coupler curves of pin-jointed Gr¨ubler kinematic chains. All these techniques and results together are contributions to theoretical kinematics of mechanisms, robot kinematics, and distance plane geometry. equations that defines the location of each link based, mainly, on independent loop equations. In the analytical approaches, the system of kinematic equations is reduced to a polynomial, known as the characteristic polynomial of the linkage, using different elimination methods —e.g., Gr¨obner bases or resultant techniques. In the numerical approaches, the system of kinematic equations is solved using, for instance, polynomial continuation or interval-based procedures. In any case, the use of independent loop equations to solve the position analysis of kinematic chains, almost a standard in kinematics of mechanisms, has seldom been questioned despite the resulting system of kinematic equations becomes quite involved even for simple linkages. Moreover, stating the position analysis of kinematic chains directly in terms of poses, with or without using independent loop equations, introduces two major disadvantages: arbitrary reference frames has to be included, and all formulas involve translations and rotations simultaneously. This thesis departs from this standard approach by, instead of directly computing Cartesian locations, expressing the original position problem as a system of distance-based constraints that are then solved using analytical and numerical procedures adapted to their particularities. In favor of developing the basics and theory of the proposed approach, this thesis focuses on the study of the most fundamental planar kinematic chains, namely, Baranov trusses, Assur kinematic chains, and pin-jointed Gr¨ubler kinematic chains. The results obtained have shown that the novel developed techniques are promising tools for the position analysis of kinematic chains and related problems. For example, using these techniques, the characteristic polynomials of most of the cataloged Baranov trusses can be obtained without relying on variable eliminations or trigonometric substitutions and using no other tools than elementary algebra. An outcome in clear contrast with the complex variable eliminations require when independent loop equations are used to tackle the problem. The impact of the above result is actually greater because it is shown that the characteristic polynomial of a Baranov truss, derived using the proposed distance-based techniques, contains all the necessary and sufficient information for solving the positionEsta tesis aborda el problema de análisis de posición de cadenas cinemáticas, mecanismos con cuerpos rígidos (enlaces) interconectados por pares cinemáticos (articulaciones). Este problema, de naturaleza geométrica, consiste en encontrar los modos de ensamblaje factibles que una cadena cinemática puede adoptar. Un modo de ensamblaje es una transformación relativa posible entre los enlaces de una cadena cinemática. Los métodos reportados en la literatura para la solución del análisis de posición de cadenas cinemáticas se pueden clasificar como gráficos, analíticos o numéricos. Los enfoques gráficos son geométricos y se diseñan para resolver problemas particulares. Los métodos analíticos y numéricos tratan con cadenas cinemáticas de cualquier topología y traducen el problema geométrico original en un sistema de ecuaciones cinemáticas que define la ubicación de cada enlace, basado generalmente en ecuaciones de bucle independientes. En los enfoques analíticos, el sistema de ecuaciones cinemáticas se reduce a un polinomio, conocido como el polinomio característico de la cadena cinemática, utilizando diferentes métodos de eliminación. En los métodos numéricos, el sistema se resuelve utilizando, por ejemplo, la continuación polinomial o procedimientos basados en intervalos. En cualquier caso, el uso de ecuaciones de bucle independientes, un estándar en cinemática de mecanismos, rara vez ha sido cuestionado a pesar de que el sistema resultante de ecuaciones es bastante complicado, incluso para cadenas simples. Por otra parte, establecer el análisis de la posición de cadenas cinemáticas directamente en términos de poses, con o sin el uso de ecuaciones de bucle independientes, presenta dos inconvenientes: sistemas de referencia arbitrarios deben ser introducidos, y todas las fórmulas implican traslaciones y rotaciones de forma simultánea. Esta tesis se aparta de este enfoque estándar expresando el problema de posición original como un sistema de restricciones basadas en distancias, en lugar de directamente calcular posiciones cartesianas. Estas restricciones son posteriormente resueltas con procedimientos analíticos y numéricos adaptados a sus particularidades. Con el propósito de desarrollar los conceptos básicos y la teoría del enfoque propuesto, esta tesis se centra en el estudio de las cadenas cinemáticas planas más fundamentales, a saber, estructuras de Baranov, cadenas cinemáticas de Assur, y cadenas cinemáticas de Grübler. Los resultados obtenidos han demostrado que las técnicas desarrolladas son herramientas prometedoras para el análisis de posición de cadenas cinemáticas y problemas relacionados. Por ejemplo, usando dichas técnicas, los polinomios característicos de la mayoría de las estructuras de Baranov catalogadas se puede obtener sin realizar eliminaciones de variables o sustituciones trigonométricas, y utilizando solo álgebra elemental. Un resultado en claro contraste con las complejas eliminaciones de variables que se requieren cuando se utilizan ecuaciones de bucle independientes. El impacto del resultado anterior es mayor porque se demuestra que el polinomio característico de una estructura de Baranov, derivado con las técnicas propuestas, contiene toda la información necesaria y suficiente para resolver el análisis de posición de las cadenas cinemáticas de Assur que resultan de la sustitución de algunas de sus articulaciones de revolución por articulaciones prismáticas. De esta forma, se concluye que los polinomios de todos los robots planares totalmente paralelos se pueden derivar directamente del polinomio característico del conocido robot 3-RPR. Adicionalmente, se presenta un procedimiento eficaz, basado en restricciones de distancias y áreas orientadas, y argumentos geométricos, para trazar curvas de acoplador de cadenas cinemáticas de Grübler. En conjunto, todas estas técnicas y resultados constituyen contribuciones a la cinemática teórica de mecanismos, la cinemática de robots, y la geometría plana de distancias. Barcelona 13