Numerical Continuation on a Graphical Processing Unit for Kinematic Synthesis

[1]  B. Roth,et al.  Synthesis of Path-Generating Mechanisms by Numerical Methods , 1963 .

[2]  Marco Pavone,et al.  Real-time stochastic kinodynamic motion planning via multiobjective search on GPUs , 2016, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[3]  Tien-Yien Li,et al.  HOM4PS-2.0para: Parallelization of HOM4PS-2.0 for solving polynomial systems , 2009, Parallel Comput..

[4]  Dinesh Manocha,et al.  g-Planner: Real-time Motion Planning and Global Navigation using GPUs , 2010, AAAI.

[5]  Rüdiger Westermann,et al.  A real-time multigrid finite hexahedra method for elasticity simulation using CUDA , 2011, Simul. Model. Pract. Theory.

[6]  J. Michael McCarthy,et al.  Computational Design of Stephenson II Six-Bar Function Generators for 11 Accuracy Points , 2016 .

[7]  Jonathan D. Hauenstein,et al.  Numerically Solving Polynomial Systems with Bertini , 2013, Software, environments, tools.

[8]  A. Morgan,et al.  Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages , 1992 .

[9]  David R. Kincaid,et al.  Numerical mathematics and computing , 1980 .

[10]  A. Morgan,et al.  Solving the Kinematics of the Most General Six- and Five-Degree-of-Freedom Manipulators by Continuation Methods , 1985 .

[11]  Ferdinand Freudenstein,et al.  Numerical Solution of Systems of Nonlinear Equations , 1963, JACM.

[12]  Jan Verschelde.  Polynomial homotopy continuation with PHCpack , 2011, ACCA.

[13]  Gordon R. Pennock,et al.  Theory of Machines and Mechanisms , 1965 .

[14]  J. Michael McCarthy,et al.  Five Position Synthesis of a Slider-Crank Function Generator , 2011 .

[15]  Jan Verschelde,et al.  Accelerating polynomial homotopy continuation on a graphics processing unit with double double and quad double arithmetic , 2015, PASCO.

[16]  Masha Sosonkina,et al.  Algorithm 857: POLSYS_GLP—a parallel general linear product homotopy code for solving polynomial systems of equations , 2006, TOMS.

[17]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[18]  Hitoshi Gotoh,et al.  GPU-acceleration for Moving Particle Semi-Implicit method , 2011 .

[19]  McCarthy,et al.  Geometric Design of Linkages , 2000 .

[20]  R. Kellogg,et al.  Pathways to solutions, fixed points, and equilibria , 1983 .

[21]  Andrew J. Sommese,et al.  The numerical solution of systems of polynomials - arising in engineering and science , 2005 .

[22]  Krishna C. Gupta,et al.  A unified approach for the investigation of branch and circuit defects , 1997 .

[23]  Jan Verschelde,et al.  Evaluating Polynomials in Several Variables and their Derivatives on a GPU Computing Processor , 2012, 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum.

[24]  J. Michael McCarthy,et al.  Homotopy Directed Optimization to Design a Six-Bar Linkage for a Lower Limb with a Natural Ankle Trajectory , 2016 .

[25]  Jan Verschelde,et al.  Tracking Many Solution Paths of a Polynomial Homotopy on a Graphics Processing Unit in Double Double and Quad Double Arithmetic , 2015, 2015 IEEE 17th International Conference on High Performance Computing and Communications, 2015 IEEE 7th International Symposium on Cyberspace Safety and Security, and 2015 IEEE 12th International Conference on Embedded Software and Systems.

[26]  T. Chase,et al.  Circuits and Branches of Single-Degree-of-Freedom Planar Linkages , 1990 .

[27]  Alexander P. Morgan,et al.  A Method for Computing All Solutions to Systems of Polynomials Equations , 1983, TOMS.