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Academic literature on the topic 'Jacobian matrix'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Jacobian matrix"

1

Xu, Yong-Xian, D. Kohli, and Tzu-Chen Weng. "Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses." Journal of Mechanical Design 116, no. 2 (June 1, 1994): 614–21. http://dx.doi.org/10.1115/1.2919422.

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A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulation leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.

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López, M., E. Castillo, G. García, and A. Bashir. "Delta robot: Inverse, direct, and intermediate Jacobians." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220, no. 1 (January 1, 2006): 103–9. http://dx.doi.org/10.1243/095440606x78263.

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In the context of a parallel manipulator, inverse and direct Jacobian matrices are known to contain information which helps us identify some of the singular configurations. In this article, we employ kinematic analysis for the Delta robot to derive the velocity of the end-effector in terms of the angular joint velocities, thus yielding the Jacobian matrices. Setting their determinants to zero, several undesirable postures of the manipulator have been extracted. The analysis of the inverse Jacobian matrix reveals that singularities are encountered when the limbs belonging to the same kinematic chain lie in a plane. Two of the possible configurations which correspond to this condition are when the robot is completely extended or contracted, indicating the boundaries of the workspace. Singularities associated with the direct Jacobian matrix, which correspond to relatively more complicated configurations of the manipulator, have also been derived and commented on. Moreover, the idea of intermediate Jacobian matrices have been introduced that are simpler to evaluate but still contain the information of the singularities mentioned earlier in addition to architectural singularities not contemplated in conventional Jacobians.

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Niitsuma, Hiroshi. "Jacobian matrix and p-basis." Banach Center Publications 26, no. 2 (1990): 185–88. http://dx.doi.org/10.4064/-26-2-185-188.

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Fang, Wang, Yang Zhen, Q. S. Kang, Shang Dong Xi, and Lin Yang Shang. "A Simulation Research on the Visual Servo Based on Pseudo-Inverse of Image Jacobian Matrix for Robot." Applied Mechanics and Materials 494-495 (February 2014): 1212–15. http://dx.doi.org/10.4028/www.scientific.net/amm.494-495.1212.

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The image Jacobian Matrix must obtain during the course of uncalibrated visual servo for classic algorithms firstly. Then the inverse of image Jacobian Matrix or pseudo-inverse of image Jacobian Matrix can be taken. But when the inverse of image Jacobian Matrix is not exist or pseudo-inverse of image Jacobian Matrix is not easy to get, the uncalibrated visual servo for robot can not realize. In this paper, a research is carried on by simulation between the classic method for uncalibrared visual servo and the strategy by computing pseudo-inverse of image Jacobian Matrix. It is conclusion that the latter not only has advantage of the performance for tracking, but also reduces computational complexity for control.

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LIU, Zhizhong. "Jacobian Matrix Normalization Based on Variable Weighting Matrix." Journal of Mechanical Engineering 50, no. 23 (2014): 29. http://dx.doi.org/10.3901/jme.2014.23.029.

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Kim, S. S., and M. J. Vanderploeg. "QR Decomposition for State Space Representation of Constrained Mechanical Dynamic Systems." Journal of Mechanisms, Transmissions, and Automation in Design 108, no. 2 (June 1, 1986): 183–88. http://dx.doi.org/10.1115/1.3260800.

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This paper presents a numerical solution method for dynamic analysis of constrained mechanical systems. This method reduces a coupled set of differential and algebraic equations to state space form. The reduction uses an independent set of velocities which lie on the tangent plane of the constraint surface. The tangent plane is defined by the nullspace of constraint Jacobian matrix. The nullspace basis is found using QR decomposition of the constraint Jacobian matrix. Because the nullspace basis is not unique, directional continuity of the nullspace is difficult to preserve each time the Jacobiar is decomposed. This paper presents an updating algorithm that is used instead oj repeated decomposition. This preserves directional continuity of the Jacobian matrix and increases efficiency. State equations are then derived in terms of independent accelerations and therefore can efficiently be integrated. Generalized velocities are integrated with constraints to obtain positions. This method has demonstrated minimal constraint violations and improved efficiency. Numerical examples with singular configurations and redundant constraints are presented to demonstrate the effectiveness of the method.

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Leung, A. Y. T., and T. Ge. "Toeplitz Jacobian Matrix for Nonlinear Periodic Vibration." Journal of Applied Mechanics 62, no. 3 (September 1, 1995): 709–17. http://dx.doi.org/10.1115/1.2897004.

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The main difference between a linear system and a nonlinear system is in the non-uniqueness of solutions manifested by the singular Jacobian matrix. It is important to be able to express the Jacobian accurately, completely, and efficiently in an algorithm to analyze a nonlinear system. For periodic response, the incremental harmonic balance (IHB) method is widely used. The existing IHB methods, however, requiring double summations to form the Jacobian matrix, are often extremely time-consuming when higher order harmonic terms are retained to fulfill the completeness requirement. A new algorithm to compute the Jacobian is to be introduced with the application of fast Fourier transforms (FFT) and Toeplitz formulation. The resulting Jacobian matrix is constructed explicitly by three vectors in terms of the current Fourier coefficients of response, depending respectively on the synchronizing mass, damping, and stiffness functions. The part of the Jacobian matrix depending on the nonlinear stiffness is actually a Toeplitz matrix. A Toeplitz matrix is a matrix whose k, r position depends only on their difference k-r. The other parts of the Jacobian matrix depending on the nonlinear mass and damping are Toeplitz matrices modified by diagonal matrices. If the synchronizing mass is normalized in the beginning, we need only two real vectors to construct the Toeplitz Jacobian matrix (TJM), which can be treated in one complex fast Fourier transforms. The present method of TJM is found to be superior in both computation time and storage than all existing IHB methods due to the simplified explicit analytical form and the use of FFT.

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van den Essen, Arno, and Engelbert Hubbers. "Polynomial maps with strongly nilpotent Jacobian matrix and the Jacobian conjecture." Linear Algebra and its Applications 247 (November 1996): 121–32. http://dx.doi.org/10.1016/0024-3795(95)00095-x.

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Reutenauer, Christophe. "Applications of a noncommutative jacobian matrix." Journal of Pure and Applied Algebra 77, no. 2 (February 1992): 169–81. http://dx.doi.org/10.1016/0022-4049(92)90083-r.

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Chèze, G., and S. Najib. "Indecomposability of polynomials via Jacobian matrix." Journal of Algebra 324, no. 1 (July 2010): 1–11. http://dx.doi.org/10.1016/j.jalgebra.2010.01.007.

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Dissertations / Theses on the topic "Jacobian matrix"

1

葛彤 and Tong Ge. "Toeplitz Jacobian matrix and nonlinear dynamical systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31234860.

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Ge, Tong. "Toeplitz Jacobian matrix and nonlinear dynamical systems /." Hong Kong : University of Hong Kong, 1996. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18987977.

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Billups, Stephen C. "An augmented Jacobian matrix algorithm for tracking homotopy zero curves." Thesis, Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/90914.

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There are algorithms for finding zeros or fixed points of nonlinear systems of (algebraic) equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. The augmented Jacobian matrix algorithm is part of the software package HOMPACK, and is based on an algorithm developed by W.C. Rheinboldt. The algorithm exists in two forms-one for dense Jacobian matrices, and the other for sparse Jacobian matrices.
M.S.

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Bourji, Samih Kassem. "Least-Change Secant Updates of Non-Square Matrices." DigitalCommons@USU, 1987. https://digitalcommons.usu.edu/etd/6989.

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In many problems involving the solution of a system of nonlinear equations, it is necessary to keep an approximation to the Jacobian matrix which is updated at each iteration. Computational experience indicates that the best updates are those that minimize some reasonable measure of the change to the current Jacobian approximation subject to the new approximation obeying a secant condition and perhaps some other approximation properties such as symmetry. All of the updates obtained thus far deal with updating an approximation to an nxn Jacobian matrix. In this thesis we consider extending most of the popular updates to the non-square case. Two applications are immediate: between-step updating of the approximate Jacobian of f(X,t) in a non-autonomous ODE system, and solving nonlinear systems of equations which depend on a parameter, such as occur in continuation methods. Both of these cases require extending the present updates to include the nx(n+l) Jacobian matrix, which is the issue we address here. Our approach is to stay with the least change secant formulation. Computational results for these new updates are also presented to illustrate their convergence behavior.

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KHER, SAMEER. "IMPROVING ANALOG SIMULATION SPEED USING THE SELECTIVE MATRIX UPDATE APPROACH IN A VHDL-AMS SIMULATOR." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1107287248.

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Jones, Jeffrey S. "Analysis of Algorithms for Star Bicoloring and Related Problems." Ohio University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1426770501.

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Korkmaz, Lale. "Static Force Production Analysis in a 3D Musculoskeletal Model of the Cat Hindlimb." Thesis, Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5193.

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To understand control strategies employed by the central nervous system (CNS) control movement or force generation in a limb, a seven degree of freedom cat hindlimb was modeled. In this study, the biomechanical constraints affecting force generation for balance and postural control were investigated. Due to the redundancies at the muscular and joint levels in the musculoskeletal system, even the muscle coordination pattern to statically produce a certain amount of force/torque at the ground is not straightforward. A 3D musculoskeletal model of the cat hindlimb was created from cat cadaver measurements using Software for Interactive Musculoskeletal Systems (SIMM, Musculographics, Inc.). Six kinematic degrees of freedom and 31 individual hindlimb muscles were modeled. The moment arms of the muscles were extracted from the software model to be used in a linear transformation between muscle activation, and end effector force and moment. The Jacobian matrix that establishes the relationship between joint torques and end effector wrench was calculated. Maximal muscle forces were estimated from the literature. A feasible set of forces that can be generated at the toe was constructed using combination of maximally activated muscle excitations. Because the endpoint torque is typically small in a cat, an optimization algorithm was also performed to maximize the force generation at the end effector while constraining the magnitude of the endpoint torque. The results are compared with the measured force magnitude and direction data from an acute cat hindlimb preparation for different postures. This static model is applicable for understanding muscle coordination during postural responses to small balance perturbations.

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Onur, Omer. "Effect Of Jacobian Evaluation On Direct Solutions Of The Euler Equations." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/2/1098268/index.pdf.

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A direct method is developed for solving the 2-D planar/axisymmetric Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes, and the resulting nonlinear system of equations are solved using Newton&
#8217
s Method. Both analytical and numerical methods are used for Jacobian calculations. Numerical method has the advantage of keeping the Jacobian consistent with the numerical flux vector without extremely complex or impractical analytical differentiations. However, numerical method may have accuracy problem and may need longer execution time. In order to improve the accuracy of numerical method detailed error analyses were performed. It was demonstrated that the finite-difference perturbation magnitude and computer precision are the most important parameters that affect the accuracy of numerical Jacobians. A relation was developed for optimum perturbation magnitude that can minimize the error in numerical Jacobians. Results show that very accurate numerical Jacobians can be calculated with optimum perturbation magnitude. The effects of the accuracy of numerical Jacobians on the convergence of flow solver are also investigated. In order to reduce the execution time for numerical Jacobian evaluation, flux vectors with perturbed flow variables are calculated for only related cells. A sparse matrix solver based on LU factorization is used for the solution, and to improve the Jacobian matrix solution some strategies are considered. Effects of different flux splitting methods, higher-order discretizations and several parameters on the performance of the solver are analyzed.

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Meyer, Arnd. "Stable evaluation of the Jacobians for curved triangles." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600629.

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In the adaptive finite element method, the solution of a p.d.e. is approximated from finer and finer meshes, which are controlled by error estimators. So, starting from a given coarse mesh, some elements are subdivided a couple of times. We investigate the question of avoiding instabilities which limit this process from the fact that nodal coordinates of one element coincide in more and more leading digits. In a previous paper the stable calculation of the Jacobian matrices of the element mapping was given for straight line triangles, quadrilaterals and hexahedrons. Here, we generalize this ideas to linear and quadratic triangles on curved boundaries.

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Cao, Weiran. "Linear Modeling of DFIGs and VSC-HVDC Systems." Thesis, KTH, Elektrisk energiomvandling, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-177643.

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Recently, with growing application of wind power, the system based on the doubly fedinduction generator (DFIG) has become the one of the most popular concepts. Theproblem of connecting to the grid is also gradually revealed. As an effective solution toconnect offshore wind farm, VSC-HVDC line is the most suitable choice for stabilityreasons. However, there are possibilities that the converter of a VSC-HVDC link canadversely interact with the wind turbine and generate poorly damped sub-synchronousoscillations. Therefore, this master thesis will derive the linear model of a single DFIG aswell as the linear model of several DFIGs connecting to a VSC-HVDC link. For thelinearization method, the Jacobian transfer matrix modeling method will be explainedand adopted. The frequency response and time-domain response comparison betweenthe linear model and the identical system in PSCAD will be presented for validation.
Nyligen, med ökande tillämpning av vindkraft, det system som bygger på den dubbeltmatad induktion generator (DFIG) har blivit en av de mest populära begrepp. Problemetmed att ansluta till nätet är också gradvis avslöjas. Som en effektiv lösning för att anslutavindkraftpark är VSC -HVDC linje det lämpligaste valet av stabilitetsskäl. Det finns dockmöjligheter att omvandlaren en VSC-HVDC länk negativt kan interagera medvindturbinen och genererar dåligt dämpade under synkron svängningar. Därför kommerdetta examensarbete härleda den linjära modellen av en enda DFIG liksom den linjäramodellen av flera DFIGs ansluter till en VSC-HVDC -länk. För arise metoden kommerJacobian transfer matrix modelleringsmetodförklaras och antas. Jämförelse mellan denlinjära modellen och identiskt system i PSCAD frekvensgången och tidsdomänensvarkommer att presenteras för godkännande.

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Books on the topic "Jacobian matrix"

1

Reider, Igor. Nonabelian Jacobian of Projective Surfaces: Geometry and Representation Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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Vinokur, Marcel. Flux Jacobian matrices and generalized Roe average for an equilibrium real gas. Washington, D. C: NASA, 1988.

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Jacobians of matrix transformations and functions of matrix argument. Singapore: World Scientific Pub., 1997.

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Engel, Andreas. Taylorentwicklung, Jacobi-Matrix, ∇, δ(x) und Co. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-59752-1.

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Almazán, Vicente. Alsacia jacobea: Introducción al estudio de las peregrinaciones alsacianas a Santiago de Compostela : historia, literatura, arte. Vigo, Galicia: Nigra Arte, 1994.

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Litvinov, G. L. (Grigoriĭ Lazarevich), 1944- editor of compilation and Sergeev, S. N., 1981- editor of compilation, eds. Tropical and idempotent mathematics and applications: International Workshop on Tropical and Idempotent Mathematics, August 26-31, 2012, Independent University, Moscow, Russia. Providence, Rhode Island: American Mathematical Society, 2014.

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Center, Ames Research, ed. Flux Jacobian matrices and generalized Roe average for an equilibrium real gas. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1989.

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8

Tanasa, Adrian. Combinatorial Physics. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895493.001.0001.

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After briefly presenting (for the physicist) some notions frequently used in combinatorics (such as graphs or combinatorial maps) and after briefly presenting (for the combinatorialist) the main concepts of quantum field theory (QFT), the book shows how algebraic combinatorics can be used to deal with perturbative renormalisation (both in commutative and non-commutative quantum field theory), how analytic combinatorics can be used for QFT issues (again, for both commutative and non-commutative QFT), how Grassmann integrals (frequently used in QFT) can be used to proCve new combinatorial identities (generalizing the Lindström–Gessel–Viennot formula), how combinatorial QFT can bring a new insight on the celebrated Jacobian conjecture (which concerns global invertibility of polynomial systems) and so on. In the second part of the book, matrix models, and tensor models are presented to the reader as QFT models. Several tensor model results (such as the implementation of the large N limit and of the double-scaling limit for various such tensor models, N being here the size of the tensor) are then exposed. These results are natural generalizations of results extensively used by theoretical physicists in the study of matrix models and they are obtained through intensive use of combinatorial techniques (this time mainly enumerative techniques). The last part of the book is dedicated to the recently discovered relation between tensor models and the holographic Sachdev–Ye–Kitaev model, model which has been extensively studied in the last years by condensed matter and by high-energy physicists.

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Engel, Andreas. Taylorentwicklung, Jacobi-Matrix, ∇, δ und Co.: Rechenmethoden für Studierende der Physik. Springer Spektrum, 2020.

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Anderson, Greg W. Spectral statistics of orthogonal and symplectic ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.5.

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This article describes a direct approach for computing scalar and matrix kernels, respectively for the unitary ensembles on the one hand and the orthogonal and symplectic ensembles on the other hand, leading to correlation functions and gap probabilities. In the classical orthogonal polynomials (Hermite, Laguerre, and Jacobi), the matrix kernels for the orthogonal and symplectic ensemble are expressed in terms of the scalar kernel for the unitary case, using the relation between the classical orthogonal polynomials going with the unitary ensembles and the skew-orthogonal polynomials going with the orthogonal and symplectic ensembles. The article states the fundamental theorem relating the orthonormal and skew-orthonormal polynomials that enter into the Christoffel-Darboux kernels

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Book chapters on the topic "Jacobian matrix"

1

Resendis-Antonio, Osbaldo. "Jacobian Matrix." In Encyclopedia of Systems Biology, 1061–62. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_1367.

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Lin, Psang Dain. "Optical Path Length and Its Jacobian Matrix." In Advanced Geometrical Optics, 353–69. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2299-9_14.

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Notash, Leila. "On the Perturbation of Jacobian Matrix of Manipulators." In Advances on Theory and Practice of Robots and Manipulators, 63–71. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07058-2_8.

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Yoshida, Kazuya, and Yoji Umetani. "Control of Space Manipulators with Generalized Jacobian Matrix." In The Kluwer International Series in Engineering and Computer Science, 165–204. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4615-3588-1_7.

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Hsieh, Yi-Zeng, Mu-Chun Su, and Yu-Lin Jeng. "The Jacobian Matrix-Based Learning Machine in Student." In Emerging Technologies for Education, 469–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71084-6_55.

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Rill, Georg. "Smoothing discontinuities in the Jacobian Matrix by Global Derivatives." In Non-smooth Problems in Vehicle Systems Dynamics, 253–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01356-0_22.

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Xin, Hongbing, Qiang Huang, Xingguang Duan, and Yueqing Yu. "A New Expression to Construct Jacobian Matrix of Parallel Mechanism." In Intelligent Robotics and Applications, 111–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-88513-9_13.

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Qi, Lizhe, Leibin Yu, Wei Wang, Lei Chen, and Chao Yun. "Analysis of the Robot Positioning Error Based on Jacobian Matrix." In Advances in Mechanical and Electronic Engineering, 329–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31507-7_54.

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Jing, Liping, Dong Deng, and Jian Yu. "Weighting Exponent Selection of Fuzzy C-Means via Jacobian Matrix." In Knowledge Science, Engineering and Management, 115–26. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12096-6_11.

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Ipbuker, Cengizhan. "Inverse Transformation for Several Pseudo-cylindrical Map Projections Using Jacobian Matrix." In Computational Science and Its Applications – ICCSA 2009, 553–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02454-2_40.

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Conference papers on the topic "Jacobian matrix"

1

Sovizi, Javad, Aliakbar Alamdari, and Venkat N. Krovi. "A Random Matrix Approach to Manipulator Jacobian." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-3950.

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Traditional kinematic analysis of manipulators, built upon a deterministic articulated kinematic modeling often proves inadequate to capture uncertainties affecting the performance of the real robotic systems. While a probabilistic framework is necessary to characterize the system response variability, the random variable/vector based approaches are unable to effectively and efficiently characterize the system response uncertainties. Hence in this paper, we propose a random matrix formulation for the Jacobian matrix of a robotic system. It facilitates characterization of the uncertainty model using limited system information in addition to taking into account the structural inter-dependencies and kinematic complexity of the manipulator. The random Jacobian matrix is modeled such that it adopts a symmetric positive definite random perturbation matrix. The maximum entropy principle permits characterization of this perturbation matrix in the form of a Wishart distribution with specific parameters. Comparing to the random variable/vector based schemes, the benefits now include: incorporating the kinematic configuration and complexity in the probabilistic formulation, achieving the uncertainty model using limited system information (mean and dispersion parameter), and realizing a faster simulation process. A case study of a 6R serial manipulator (PUMA 560) is presented to highlight the critical aspects of the process. A Monte Carlo analysis is performed to capture the deviations of distal path from the desired trajectory and the statistical analysis on the realizations of the end effector position and orientation shows how the uncertainty propagates throughout the system.

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Xu, Yong-Xian, Dilip Kohli, and Tzu-Chen Weng. "Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0199.

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Abstract A general formulation for the differential kinematics of hybrid-chain manipulators is developed based on transformation matrices. This formulations leads to velocity and acceleration analyses, as well as to the formation of Jacobians for singularity and unstable configuration analyses. A manipulator consisting of n nonsymmetrical subchains with an arbitrary arrangement of actuators in the subchain is called a hybrid-chain manipulator in this paper. The Jacobian of the manipulator (called here the system Jacobian) is a product of two matrices, namely the Jacobian of a leg and a matrix M containing the inverse of a matrix Dk, called the Jacobian of direct kinematics. The system Jacobian is singular when a leg Jacobian is singular; the resulting singularity is called the inverse kinematic singularity and it occurs at the boundary of inverse kinematic solutions. When the Dk matrix is singular, the M matrix and the system Jacobian do not exist. The singularity due to the singularity of the Dk matrix is the direct kinematic singularity and it provides positions where the manipulator as a whole loses at least one degree of freedom. Here the inputs to the manipulator become dependent on each other and are locked. While at these positions, the platform gains at least one degree of freedom, and becomes statically unstable. The system Jacobian may be used in the static force analysis. A stability index, defined in terms of the condition number of the Dk matrix, is proposed for evaluating the proximity of the configuration to the unstable configuration. Several illustrative numerical examples are presented.

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Wang, Xiaozhe, and Konstantin Turitsyn. "PMU-based estimation of dynamic state Jacobian matrix." In 2017 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2017. http://dx.doi.org/10.1109/iscas.2017.8050926.

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Daher, Nivine Abou, Imad Mougharbel, Maarouf Saad, Hadi Y. Kanaan, and Dalal Asber. "Pilot buses selection based on reduced Jacobian matrix." In 2015 IEEE International Conference on Smart Energy Grid Engineering (SEGE). IEEE, 2015. http://dx.doi.org/10.1109/sege.2015.7324611.

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Kolka, Zdenek, Viera Biolkova, Zdenek Kincl, and Dalibor Biolek. "Parametric reduction of Jacobian matrix for fault analysis." In 2010 International Conference on Microelectronics (ICM). IEEE, 2010. http://dx.doi.org/10.1109/icm.2010.5696200.

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Hosseinzadegan, Samar, Shireen Geimer, Andreas Fhager, Mikael Persson, and Paul Meaney. "Fast Jacobian Matrix Formulation for Microwave Tomography Applications." In 2021 15th European Conference on Antennas and Propagation (EuCAP). IEEE, 2021. http://dx.doi.org/10.23919/eucap51087.2021.9411451.

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Lu, Yi, and Bo Hu. "Solving Jacobian Matrix of Parallel Manipulators With Linear Driving Limbs by Using CAD Variation Geometric Approach." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99019.

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Abstract:

The velocity Jacobian matrix and the force Jacobian matrix are important index for kinematics, singularity and dynamics analyses of parallel manipulators. A novel computer variation geometric approach is proposed for solving the velocity Jacobian matrix and the force Jacobian matrix of parallel manipulators with linear driving limbs, as well as the determinant of Jacobian matrix. First, basic computer variation geometry techniques and definitions are presented for designing the simulation mechanisms, and several simulation mechanisms of parallel manipulators with linear driving limbs are created. Second, some velocity simulation mechanisms are created and the partial derivatives in Jacobian matrix are solved automatically and visualized dynamically. Based on the results of the computer simulation, the velocity Jacobian matrix and force Jacobian matrix are formed and the determinant of Jacobian matrix is solved. Moreover, the simulation results prove that the computer variation geometry approach is fairly quick and straightforward, and is accurate and repeatable. This project is supported by NSFC No. 50575198.

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Abdi, Hamid, Saeid Nahavandi, and Anthony A. Maciejewski. "Optimal fault-tolerant Jacobian matrix generators for redundant manipulators." In 2011 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2011. http://dx.doi.org/10.1109/icra.2011.5979802.

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Brown, Brandon, Tarunraj Singh, and Rahul Rai. "Pareto Front Identification via Objective Vector Jacobian Matrix Singularity." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12271.

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This paper presents a method to identify the exact Pareto front for a multi-objective optimization problem. The developed technique addresses the identification of the Pareto frontier in the cost space and the Pareto set in the design space for both constrained and unconstrained optimization problems. The proposed approach identifies a n – 1 dimensional hypersurface for a multi-objective problem with n cost functions, a subset of which constitute the Pareto front. The n – 1 dimensional hypersurface is identified by enforcing a singularity constraint on the Jacobian of the cost vector with respect to the optimization parameters. Since the boundary is identified in the design space, the relation of design points to the exact Pareto front in the cost space is known. The proposed method is proven effective in the Pareto identification for a set of previously released challenge problems. Six of these examples are included in this paper; 3 unconstrained and 3 constrained.

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Cinquemani, Simone, Hermes Giberti, and Giovanni Legnani. "The Generalized Jacobian Matrix and the Manipulators Kinetostatic Properties." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24919.

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Manipulator kinetostatic performances are usually investigated considering only the geometrical structure of the robot, neglecting the effect of the drive system. In some circumstances this approach may leads to errors and mistakes. This may happen if the actuators are not identical to each other or when the employed transmission ratio are not identical and/or not constant. The paper introduces the so called “Generalized Jacobian Matrix” obtained identifying an appropriate matrix, generally diagonal, defined in order to: 1. properly weigh the different contributions of speed and force of each actuator. 2. describe the possible non-homogeneous behaviour of the drive system that depends on the configuration achieved by the robot. Theoretical analysis is supported by examples highlighting some of the most common mistakes done in the evaluation of a manipulator kinetostatic properties and how they can be avoided using the generalized jacobian matrix.

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Reports on the topic "Jacobian matrix"

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Eydenberg, Michael, Kanad Khanna, and Ryan Custer. Effects of Jacobian Matrix Regularization on the Detectability of Adversarial Samples. Office of Scientific and Technical Information (OSTI), December 2020. http://dx.doi.org/10.2172/1763568.

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