Measuring the closeness to singularities of a planar parallel manipulator using geometric algebra

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

doi:10.1016/j.apm.2018.01.006

Cited by 9 publications

(6 citation statements)

References 24 publications

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“…[19][20][21][22][23] In the framework of G 6 , the twist space and wrench space were described symbolically by Li et al 24,25 and were used to construct the expanded blade of limb constraint (EBLC) of PMs. [26][27][28] The original constraint wrenches and converted transmission wrenches are encompassed within the EBLC. However, this method cannot be applied to MCMs directly because of the coupled chains in MCMs.…”

Section: Introductionmentioning

confidence: 99%

Actuation selection for multi-loop coupling mechanisms using geometric algebra

Chai,

Xiao,

et al. 2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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Multi-loop coupling mechanisms (MCMs) have been widely used in architectural design antennas and space-deployable. This paper proposes a general method for actuation selection of MCMs using geometric algebra. The constraint space is obtained by collineation and dual operators of twist space. This method determines additional constraints by analyzing the linear correlation between the constrained spaces of the two limbs within the closed-loop and making corrections to the constraint space of the basic limb. Through outer and dual operators, the input screw corresponding to the transmission wrench screw and output twist screw are obtained. The input transmission index (ITI) and output transmission index (OTI) corresponding to this input are calculated, which leads to generation of a local transmission index (LTI). The actuation selection with the best performance can be obtained by comparing and analyzing the motion/force transfer performance of all input combinations. The proposed method has the advantages of simple computation and clear physical significance, and three typical MCMs are applied to validate this method. Finally, an experimental analysis compared the power consumption of a test motor at different actuation positions, further proving the accuracy of the method.

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Section: Introductionmentioning

confidence: 99%

Actuation selection for multi-loop coupling mechanisms using geometric algebra

Chai,

Xiao,

et al. 2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…In the practical application, it is also needed to detect how far the end-effector stays away from the singular configurations. Therefore, some effective evaluation indexes measuring the closeness 11,12 to singularity are proposed.…”

Section: Introductionmentioning

confidence: 99%

Self-excited vibration of a 3-PRR planar parallel robot

Zhu

Qiu

Xie

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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Self-excited vibration of parallel robots can seriously affect the motion performance and damage the mechanical structure. In order to study the self-excited vibration characteristics of a 3-PRR (where P and R represent the prismatic and revolute joints respectively and the underlined letter represents the actuated joint) planar parallel robot, dynamic model is firstly established and the singularity is analyzed theoretically. Then the dynamic characteristics at internal and boundary singularities are both explored experimentally. The motion form and generating mechanism of the self-excited vibration are researched. The influencing factors on vibration frequency are obtained and the self-excited vibration during trajectory tracking motion is analyzed. Finally, a singularity escaping strategy is proposed and tested. Theoretical analysis and experimental results show that the performance of parallel robot deteriorates dramatically at singularities. Nevertheless, the parallel robot can pass through the internal singularity successfully with optimized load and motion speed so that the workspace can be expanded. The 3-PRR planar parallel robot exhibits self-excited vibration at internal singularities, which is mainly caused by the singularity, self-regulation of motors and the closed-chain coupling effect. The vibration frequency is mainly determined by singular configuration and the structural parameters. The parallel robot can maintain self-excited vibration state while carrying out trajectory tracking under a singular attitude angle. Moreover, the proposed singularity escaping strategy is verified to be feasible so that the self-excited vibration can be eliminated effectively.

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“…Although there are several approaches based on the use of such indexes [23,24], none of them defines a distance function and, as stated in [25], they do not provide a realistic measure of how close a singularity is, just whether it is close or not. On the other hand, Yao et al [26] propose a different index of closeness to singularities for planar parallel robots based on the volume of the workspace. Despite interesting, it is still not a distance function and it can neither be easily applied to serial robots.…”

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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Measuring the closeness to singularities of a planar parallel manipulator using geometric algebra

Cited by 9 publications

References 24 publications

Actuation selection for multi-loop coupling mechanisms using geometric algebra

Actuation selection for multi-loop coupling mechanisms using geometric algebra

Self-excited vibration of a 3-PRR planar parallel robot

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

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