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- W3081598084 abstract "Author(s): Glabe, Jeffrey | Advisor(s): McCarthy, John M | Abstract: Kinematic synthesis, at its heart, involves finding the zero-dimensional solution set of asystem of polynomials. The degree of these polynomials increases rapidly as more complex designs are considered. The computation time required to find the solution set hastraditionally been the bounding factor for what can been achieved in kinematic synthesis.Homotopy continuation is typically used to find solutions to these polynomials. Homotopycontinuation is itself an inherently parallelizable method. Graphics processing units (GPUs)were developed were developed with a structure that makes them optimal to solve problemsin parallel. This dissertation explores the use of homotopy continuation running a GPU inorder to decrease the computation time required for kinematic synthesis.First, we discuss the development of an algorithm for homotopy continuation that is idealto run on a GPU. The traditional path tracking algorithm is analyzed and then modified tobetter perform on a GPU. Additionally, the endgame methods are analyzed and the moreideal method is identified and implemented in CUDA. We outline the drawbacks of suchmodifications and discuss why they are admissible in the context of kinematic synthesis.The implementation of the new homotopy continuation algorithm on a GPU is demonstrated by solving the four-bar linkage synthesis problem. This is the first development ofa GPU-accelerated four-bar linkage design system. Novel (non-Burmester) loop equationsare derived such that the entire mechanism is solved in one computation. These equationsare then reduced and implemented into CUDA. The entire program is outlined and thendemonstrated on a sample design problem. The results are compared with a similar CPUimplemented system and a GPU speedup of around 120 times was observed.The results of the four-bar linkage design system were then extended to the problem of sixbar linkage synthesis. A system was developed utilizing the same GPU-based path trackerand endgame. This has resulted in the first known GPU-accelerated six-bar linkage designsystem that presents new opportunities for multi-GPU systems capable of designing evenmore complicated mechanisms." @default.
- W3081598084 created "2020-09-08" @default.
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- W3081598084 date "2020-01-01" @default.
- W3081598084 modified "2023-09-23" @default.
- W3081598084 title "Numerical Continuation on a GPU for Kinematic Synthesis" @default.
- W3081598084 hasPublicationYear "2020" @default.
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