A Classification of Robot Compliance

Patterson, Timothy; Lipkin, Harvey

doi:10.1115/1.2919229

Cited by 59 publications

(20 citation statements)

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“…If neither r 2 nor r 3 can cross l 1 , t 2 t T 2 and t 3 t T 3 must always be on the same side of plane P 1 defined in Eq. (11). Thus, the given C cannot be realized at that endpoint location.…”

Section: Realization Conditions For Every Compliancementioning

confidence: 86%

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Realization of point planar elastic behaviors using revolute joint serial mechanisms having specified link lengths

Huang

Schimmels

2016

Mechanism and Machine Theory

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A B S T R A C TThis paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having only revolute joints, each with selectable compliance. The link lengths of the mechanism and the location of the compliant frame relative to the mechanism base are arbitrary but specified. The realizability of a given compliant behavior is investigated, and necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. These realization conditions are interpreted in terms of geometric relationships among the joints. We show that, for an appropriately sized 3R serial mechanism, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. Requirements on mechanism geometry to realize every particle planar elastic behavior at a given location just by changing the mechanism configuration are also identified.

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Section: Realization Conditions For Every Compliancementioning

confidence: 86%

“…Screw theory [7][8][9][10][11] and Lie groups [12] have been used to analyze and characterize spatial linear elastic behavior (represented by a 6 × 6 symmetric stiffness matrix K or compliance matrix C).…”

Section: Related Workmentioning

confidence: 99%

Realization of point planar elastic behaviors using revolute joint serial mechanisms having specified link lengths

Huang

Schimmels

2016

Mechanism and Machine Theory

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“…A possible solution to this problem is the definition of a dimensionless or dimensionally consistent stiffness matrix as proposed for example in Refs. [24][25][26]. However, this would require the definition of a characteristic length L, whose choice is usually questionable but significantly affecting the results.…”

Section: Indices For Stiffness Performance Evaluationmentioning

confidence: 97%

Comparison of indices for stiffness performance evaluation

Carbone

Ceccarelli

2010

Front. Mech. Eng. China

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This paper addresses the problem of a numerical evaluation of the stiffness performance for multibody robotic systems. An overview is presented with basic formulation concerning indices that are proposed in literature. New indices are also outlined. Stiffness indices are computed and compared for a case study. Results are used for comparing the effectiveness of the stiffness indices. The main goal is to propose a performance index describing synthetically the elastostatic response of a multibody robotic system and also for design purposes.

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“…A cross-sectional area of a wire E m elastic modulus of a wire E transformation matrix of a screw expressed in axis coordinates f intensity of an applied wrench F externally applied wrench G m shear modulus of a wire h vector from the mass centre to the centre of elasticity I area moment of inertia I 363 , 0 363 363 identity and zero matrices J mass moment of inertia k x , k y , k z principal stiffnesses k a , k b , k g principal stiffnesses K E stiffness matrix measured about the centre of elasticity body have been intensively investigated by Patterson and Lipkin [1,2]. Lipkin and Patterson [3] developed a geometrical decomposition method diagonalizing the stiffness matrix by a congruence transformation.…”

Section: Notationmentioning

confidence: 99%

Vibration analysis of single rigid-body systems having planes of symmetry

Dan

Choi

2002

Proceedings of the Institution of Mechanical Engineers, Part C:

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By taking a geometrical approach to vibration analysis, the vibration mode shapes of a single rigid body may be better understood. F rom the geometrical point of view, the eigenvectors represent repetitive twisting motions on the axes of vibrations in a three-dimensional space. The frequency response can be expressed by a scalar multiple of the axis of vibration in Plu¨cker's axis coordinates, which is the reciprocal product of the axis of vibration and applied force. The geometrical interpretation of the frequency response provides the design methodology to eliminate the undesired peaks. The methodology involves making the mutual moment of the axis of vibration and applied force become zero or adjusting the location of the axes of vibrations to the sensing point. In order to implement this geometrical design method, an optical pick-up used in the information storage device has been utilized. Some numerical results show design improvement concerning the frequency response of the pick-up device and thereby the validity of the design technique.

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A Classification of Robot Compliance

Cited by 59 publications

References 0 publications

Realization of point planar elastic behaviors using revolute joint serial mechanisms having specified link lengths

Realization of point planar elastic behaviors using revolute joint serial mechanisms having specified link lengths

Comparison of indices for stiffness performance evaluation

Vibration analysis of single rigid-body systems having planes of symmetry

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