An overview of formulae for the higher-order kinematics of lower-pair chains with applications in robotics and mechanism theory

Müller, Andreas

doi:10.1016/j.mechmachtheory.2019.103594

Cited by 38 publications

(12 citation statements)

References 111 publications

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“…In this section, the concept of kinematic tangent cone to the configuration space of a mechanism is briefly revisited. Refer to [55] for a more in-depth read about the topic and to [57] for the computational aspects.…”

Section: A Brief Introduction To the Kinematic Tangent Cone Analysismentioning

confidence: 99%

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Tangential intersection of branches of motion

López-Custodio

Müller

Kang

et al. 2020

Mechanism and Machine Theory

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The branches of motion in the configuration space of a reconfigurable linkage can intersect in different ways leading to different types of singularities. In the vast majority of reported linkages whose configuration spaces contain multiple branches of motion the intersection happens transversally, allowing local methods, like the computation of its tangent cone, to identify different branches by means of their tangents. However, if these branches are of the same dimension and they intersect tangentially, it is not possible to identify them by means of the tangent cone at the singularity as the tangent spaces to the branches are the same. Although this possibility has been mentioned by a few researchers, whether linkages with this kind of tangent intersection of branches of motion exist is still an open question. In this paper, it is shown that the answer to this question is yes: A local method is proposed for the effective identification of branches of motion intersecting tangentially, and a method for the type synthesis of linkages that exhibit this particular type of singularity is presented.

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Section: A Brief Introduction To the Kinematic Tangent Cone Analysismentioning

confidence: 99%

“…represents the i-th order kinematic equation. Explicit expressions for these kinematic higher-order analyses can be found in [31,33,[57][58][59]. The kinematic tangent cone is obtained as:…”

Section: A Brief Introduction To the Kinematic Tangent Cone Analysismentioning

confidence: 99%

Tangential intersection of branches of motion

López-Custodio

Müller

Kang

et al. 2020

Mechanism and Machine Theory

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“…The pioneering work of Ball [2], the treatises of Hunt [3], and Phillips [4] and the multitude of contributions appearing in the literature are evidence of this. The isomorphism between screw theory and the Lie algebra, se(3), of the Special Euclidean group, S 3 , provide with a wealth of results and techniques from modern differential geometry and Lie group theory [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…Time derivatives of the twists of members in a kinematic chain and derivatives of screws are essential operations in kinematics. Recognizing the Lie group nature of rigid body motions, and correspondingly the Lie algebra nature of screws, Karger [5], Rico et al [6], Lerbet [7] and Müller [8,9] derived closed form expressions of higher-order time derivatives of twist.…”

Section: Introductionmentioning

confidence: 99%

Higher-Order Kinematics in Dual Lie Algebra

Condurache¹

2020

Advances on Tensor Analysis and Their Applications

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In this chapter, using the ring properties of dual number algebra, vector and tensor calculus, a computing method for the higher-order acceleration vector field properties in general rigid body motion is proposed. The higher-order acceleration field of a rigid body in a general motion is uniquely determined by higher-order time derivative of a dual twist. For the relative kinematics of rigid body motion, equations that allow the determination of the higher-order acceleration vector field are given, using an exponential Brockett-like formula in the dual Lie algebra. In particular cases, the properties for velocity, acceleration, jerk, and jounce fields are given. This approach uses the isomorphism between the Lie algebra of the rigid displacements se(3), of the Special Euclidean group, S 3 , and the Lie algebra of dual vectors. The results are coordinate free and in a closed form.

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“…For such a connection the higher-order derivatives of the loop-closure equations are found and solved yielding a Taylor approximation of finite motion [28]. In that approach, the higher-order partial derivatives of the body twists are found from the adjoint twist matrices corresponding to the ISA that are lower in the serial chain equivalent [79]. Since each ISA is constant when expressed in a local body-fixed frame, all these derivatives follow from a repetitive application of Eq.…”

Section: Higher-order Derivatives Of Kinematicsmentioning

confidence: 99%

Screw theory based dynamic balance methods

Jong¹,

Johannes²

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An overview of formulae for the higher-order kinematics of lower-pair chains with applications in robotics and mechanism theory

Cited by 38 publications

References 111 publications

Tangential intersection of branches of motion

Tangential intersection of branches of motion

Higher-Order Kinematics in Dual Lie Algebra

Screw theory based dynamic balance methods

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