Kinetostatic Analysis and Solution Classification of a Planar Tensegrity Mechanism

Tensegrity mechanisms have several interesting properties that make them suitable for a number of applications. Their analysis is generally challenging because the static equilibrium conditions often result in complex equations. A class of planar one-degree-of-freedom (dof) tensegrity mechanisms with three linear springs is analyzed in detail in this paper. The kinetostatic equations are derived and solved under several loading and geometric conditions. It is shown that these mechanisms exhibit up to six equilibrium configurations, of which one or two are stable. Discriminant varieties and cylindrical algebraic decomposition combined with Groebner base elimination are used to classify solutions as function of the input parameters.Comment: 7th IFToMM International Workshop on Computational Kinematics, May 2017, Poitiers, France. 201

The Daily Egyptian, March 21, 1996

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2006Includes bibliographical references (leaves: 78-85)Text in English; Abstract: Turkish and Englishxi, 98 leavesTheory of Machines and Mechanisms is one of the main branches of science including many sub-branches such as biomechanics, human machine systems, computational kinematics, mechatronics, robotics, design methodology, dynamics of machinery, gearings and transmissions, cams and linkages, micro machines, nonlinear oscillations, reliability of machines and mechanisms etc. In this large area of interest, this study can be matched with the sub groups biomechanics, robotics, computational kinematics and design methodology. The main concern of the thesis is the biokinematics of the human arm. In the process of design, a suitable tool for the kinematics of human arm is investigated as quaternions along with examples. Moreover, the history of the formulas of Dof is presented as 38 equations with the unique key controlling parameters that are used in the design of new Cartesian and serial platform type robot manipulators. Structural syntheses of new manipulators are considered.Simple serial platform structural groups in subspace 8.3, and general space 8.6 are presented along with examples. Furthermore, type synthesis of human arm is accomplished with the new proposed parallel manipulator for the shoulder, elbow and wrist complex. Finally, computational kinematics of the serial human wrist manipulator and the geometrical kinematic analysis of the orientation platforms of the new parallel manipulator design for the human arm are accomplished

A study of the singularity locus in the joint space of planar parallel manipulators: special focus on cusps and nodes

Cusps and nodes on plane sections of the singularity locus in the joint space of parallel manipulators play an important role in nonsingular assembly-mode changing motions. This paper analyses in detail such points, both in the joint space and in the workspace. It is shown that a cusp (resp. a node) defines a point of tangency (resp. a crossing point) in the workspace between the singular curves and the curves associated with the so-called characteristics surfaces. The study is conducted on a planar 3-RPR manipulator for illustrative purposes.Comment: 4th International Congress Design and Modeling of Mechanical Systems, Sousse : Tunisia (2011

Robustness to Algorithmic Singularities and Sensitivity in Computational Kinematics

A robust approach to computational kinematics intended to cope with algorithmic singularities is introduced in this article. The approach is based on the reduction of the original system of equations to a subsystem of bivariate equations, as opposed to the multivariate polynomial reduction leading to the characteristic univariate polynomial. The effectiveness of the approach is illustrated for the exact function-generation synthesis of planar, spherical, and spatial four-bar linkages. Some numerical examples are provided for the case of the spherical four-bar function generator with six precision points to show the benefits of the proposed method with respect to methods reported in the literature.The first author acknowledges the support of Universidad Politecnica de Valencia, research project PAID-00-09. The second author acknowledges the support of McGill University by means of a James McGill Professorship.Gracia Calandin, LI.; Angeles, J. (2011). Robustness to Algorithmic Singularities and Sensitivity in Computational Kinematics. Proceedings of the Institution of Mechanical Engineers part C - Journal of Mechanical Engineering Science. 225(4):987-999. doi:10.1243/09544062JMES2464S9879992254Raghavan, M., & Roth, B. (1993). Inverse Kinematics of the General 6R Manipulator and Related Linkages. Journal of Mechanical Design, 115(3), 502-508. doi:10.1115/1.2919218Lee, H. Y., Woernle, C., & Hiller, M. (1991). A Complete Solution for the Inverse Kinematic Problem of the General 6R Robot Manipulator. Journal of Mechanical Design, 113(4), 481-486. doi:10.1115/1.2912808Innocenti, C., & Parenti-Castelli, V. (1993). Echelon form solution of direct kinematics for the general fully-parallel spherical wrist. Mechanism and Machine Theory, 28(4), 553-561. doi:10.1016/0094-114x(93)90035-tGosselin, C. M., Sefrioui, J., & Richard, M. J. (1994). On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators of General Architecture. Journal of Mechanical Design, 116(2), 594-598. doi:10.1115/1.2919419Alizade, R. I., & Kilit, Ö. (2005). Analytical synthesis of function generating spherical four-bar mechanism for the five precision points. Mechanism and Machine Theory, 40(7), 863-878. doi:10.1016/j.mechmachtheory.2004.12.010Cervantes-Sánchez, J. J., Gracia, L., Rico-Martínez, J. M., Medellín-Castillo, H. I., & González-Galván, E. J. (2009). A novel and efficient kinematic synthesis approach of the spherical 4R function generator for five and six precision points. Mechanism and Machine Theory, 44(11), 2020-2037. doi:10.1016/j.mechmachtheory.2009.05.006Angeles, J. (2007). Fundamentals of Robotic Mechanical Systems. Mechanical Engineering Series. doi:10.1007/978-0-387-34580-2Bai, S., Hansen, M. R., & Angeles, J. (2009). A robust forward-displacement analysis of spherical parallel robots. Mechanism and Machine Theory, 44(12), 2204-2216. doi:10.1016/j.mechmachtheory.2009.07.005Sommese, A. J., & Wampler, C. W. (2005). The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. doi:10.1142/5763Forsythe, G. E. (1970). Pitfalls in Computation, or why a Math Book isn’t Enough. The American Mathematical Monthly, 77(9), 931. doi:10.2307/2318109Angeles, J., Hommel, G., & Kovács, P. (Eds.). (1993). Computational Kinematics. Solid Mechanics and Its Applications. doi:10.1007/978-94-015-8192-9Yang, A. T., & Freudenstein, F. (1964). Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms. Journal of Applied Mechanics, 31(2), 300-308. doi:10.1115/1.3629601Gupta, K. C., & Beloiu, A. S. (1998). Branch and circuit defect elimination in spherical four-bar linkages. Mechanism and Machine Theory, 33(5), 491-504. doi:10.1016/s0094-114x(97)00078-

Yet another approach to the Gough-Stewart platform forward kinematics

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The forward kinematics of the Gough-Stewart platform, and their simplified versions in which some leg endpoints coalesce, has been typically solved using variable elimination methods. In this paper, we cast doubts on whether this is the easiest way to solve the problem. We will see how the indirect approach in which the length of some extra virtual legs is first computed leads to important simplifications. In particular, we provide a procedure to solve 30 out of 34 possible topologies for a Gough-Stewart platform without variable elimination.Peer ReviewedPostprint (author's final draft

Inverse kinematics by distance matrix completion

International Workshop on Computational Kinematics (CK), 2005, Cassino (Italia)This paper characterizes a family of serial robots whose inverse kinematics can be translated into a system of distance constraints that can be solved using a sequence of constructive operations taking as fixed reference either a triangle or a tetrahedron. The relevance of the obtained family of robots is established when it is shown to contain the best-known commercial serial robots.This work was supported by the project 'Design and implementation of efficient parallelizable algorithms with applications to robotics and proteomics' (J-00869).Peer Reviewe