Singularity Analysis of 3-RPR Parallel Manipulators Using Geometric Algebra

Yao, Huijing; Chen, Qiao‐Hong; Chai, Xinxue; Li, Qinchuan

doi:10.1007/s00006-017-0794-y

Cited by 13 publications

(12 citation statements)

References 32 publications

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“…Yao et al [243] presented a novel method based on GA for the singularity analysis of 3 DOF overconstrained planar parallel manipulators 3-RPR. GA offers a compact and geometrically intuitive formulation of the singularity polynomial of the parallel manipulators 3-RPR.…”

Section: K Robotics: Kinematics Dynamics Tracking Controlmentioning

confidence: 99%

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Bayro–Corrochano

2021

IEEE Access

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Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics, computer science, and engineering. This review presents a comprehensive study of works on Quaternion Algebra and GA applications in computer science and engineering from 1995 to 2020. After a brief introduction of GA, the applications of GA are reviewed across many fields. We discuss the characteristics of the applications of GA to various problems of computer science and engineering. In addition, the challenges and prospects of various applications proposed by many researchers are analyzed. We analyze the developments using GA in image processing, computer vision, neurocomputing, quantum computing, robot modeling, control, and tracking, as well as improvement of computer hardware performance. We believe that up to now GA has proven to be a powerful geometric language for a variety of applications. Furthermore, there is evidence that this is the appropriate geometric language to tackle a variety of existing problems and that consequently, step-by-step GA-based algorithms should continue to be further developed. We also believe that this extensive review will guide and encourage researchers to continue the advancement of geometric computing for intelligent machines.INDEX TERMS Geometric algebra, Clifford algebra, quaternion algebra, screw theory, signal processing, electrical engineering and power systems, geometric and quantum computing, image processing, computer vision, graphic engineering, artificial intelligence, machine learning, neural networks, control engineering, robotics, biomedical engineering, and biotechnology.

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Section: K Robotics: Kinematics Dynamics Tracking Controlmentioning

confidence: 99%

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Bayro–Corrochano

2021

IEEE Access

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“…For parallel mechanisms, the majority of works [14,15,16,17,18] focus on approaches developed for some particular parallel robots. The main idea consists of computing, for each leg of the mechanism, the exterior product of the twists defined by its joints and equating it to zero.…”

Section: Introductionmentioning

confidence: 99%

Singularities of serial robots: Identification and distance computation using geometric algebra

Zaplana,

Hadfield,

Lasenby

2021

Preprint

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The singularities of serial robotic manipulators are those configurations in which the robot loses the ability to move in at least one direction. Hence, their identification is fundamental to enhance the performance of current control and motion planning strategies. While classical approaches entail the computation of the determinant of either a 6 × n or n × n matrix for an n degrees of freedom serial robot, this work addresses a novel singularity identification method based on modelling the twists defined by the joint axes of the robot as vectors of the six-dimensional and three-dimensional geometric algebras. In particular, it consists of identifying which configurations cause the exterior product of these twists to vanish. In addition, since rotors represent rotations in geometric algebra, once these singularities have been identified, a distance function is defined in the configuration space C such that its restriction to the set of singular configurations S allows us to compute the distance of any configuration to a given singularity. This distance function is used to enhance how the singularities are handled in three different scenarios, namely motion planning, motion control and bilateral teleoperation.

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“…X Huo et al 19 proposed a geometric algebra (GA)-based approach to determine the motions/constraints, mobility, and singularity of parallel mechanisms mainly utilizing the geometric and algebraic relations. H Yao et al 20 presented a method based on GA for the singularity of 3-DOF redundant constraints of 3-Revolute-Prismatic-Revolute (3-RPR) planar parallel manipulators. Based on screw theory, L Kang et al, 21 and W Li and J Angeles 22 demonstrated the actuator redundancies and singularities, respectively.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of three-translational degree-of-freedom spatial compliant mechanism

Zhu

Feng

Zhan

2019

Advances in Mechanical Engineering

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Considering that the Jacobian matrix maps the velocity of the joint space of the robot to the end velocity of the Cartesian space, a novel topology optimization approach is proposed in this article for the design of three-translational degree-of-freedom spatial compliant mechanisms by combining the optimized Jacobian mapping matrix with the solid isotropic material with penalization topological method. First, by using the condition number method, the structural parameters of Universal-Prismatic-Universal (UPU)-type parallel prototype manipulator are optimized, and then, the differential Jacobian mapping matrix is calculated by using equivalent infinitesimal method. Second, comparing with the driver configuration and twist/wrench constraint conditions of the UPU-type parallel prototype manipulator, the topological algorithm combining solid isotropic material with penalization with optimized Jacobian mapping matrix is proposed. Finally, a novel spatial compliant mechanism with three-translational degree-of-freedom is derived, and numerical simulation results are reported to demonstrate the effectiveness of the proposed method.

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Singularity Analysis of 3-RPR Parallel Manipulators Using Geometric Algebra

Cited by 13 publications

References 32 publications

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Singularities of serial robots: Identification and distance computation using geometric algebra

Topology optimization of three-translational degree-of-freedom spatial compliant mechanism

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