Analyse und Synthese der Raumkurbelgetriebe mittels Raumliniengeometrie und dualer Größen

Keler, M. L.

doi:10.1007/bf02557024

Cited by 10 publications

(2 citation statements)

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“…Their presence is also felt in other areas of science and engineering, which has raised interest in various aspects of linear algebra and computational methods associated with their use [12,13,14,15]. The pioneering work in the engineering applications of dual algebra is made by Keler [16], Beyer [17], etc.…”

Section: Introductionmentioning

confidence: 99%

“…MPDGI and DMPGI are used in many aspects. For example, in [16], Udwadia and Pennestrì apply MPDGI to various motions such as rigid body translation and dual angular velocity acquisition. In [15], DMPGI is applied to kinematic synthesis of spatial mechanisms, and a series of numerical examples about calculation and application of DMPGI to kinematic synthesis of linkage mechanisms are given.…”

Section: Introductionmentioning

confidence: 99%

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The Dual Index and Dual Core Generalized Inverse

Wang¹,

Gao²

2022

Preprint

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In this paper, we introduce the dual index and dual core generalized inverse (DCGI). By applying rank equation, generalized inverse and matrix decomposition, we give several characterizations of the dual index when it is equal to one. And we get that if DCGI exists, then it is unique. We derive a compact formula for DCGI and a series of equivalent characterizations of the existence of the inverse. It is worth nothing that the dual index of A is equal to one if and only if its DCGI exists. When the dual index of A is equal to one, we study dual Moore-Penrose generalized inverse (DMPGI) and dual group generalized inverse (DGGI), and consider the relationships among DCGI, DMPGI, DGGI, Moore-Penrose dual generalized inverse (MPDGI) and other dual generalized inverses. In addition, we consider symmetric dual matrix and its dual generalized inverses. At last, two examples are given to illustrate the application of DCGI in linear dual equations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Dual Index and Dual Core Generalized Inverse

Wang¹,

Gao²

2022

Preprint

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The adjoint trigonometric representation of displacements and a closed‐form solution to the IKP of general 3C chains

Bongardt

2020

Z Angew Math Mech

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Based on the representation of rigid body displacements as adjoint matrices, the article introduces the adjoint trigonometric representation of displacements (ATRD) as a further generalization of the trigonometric representation of rotations. In comparison to the dual Rodrigues–Euler–Gauß–Gelman equation, recently reported for affine screw displacements with arbitrary, fixed pitches, the ATRD is built upon a product of a unit line and a dual angle, instead of upon a product of a unit screw and a real angle. Due to this conceptual difference, the ATRD requires four independent parameters of a unit line instead of five when parametrizing a displacement along a unit screw. As a consequence for computational kinematics, the ATRD permits transferring the analytic solution to the inverse kinematics problem (IKP) of 3‐DOF, general, spherical 3R‐chains into a closed‐form solution to the IKP of 6‐DOF, general, affine 3C‐chains.

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William Kingdon Clifford (1845–1879)

Rooney¹

History of Mechanism and Machine Science

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Abstract. William Kingdon Clifford was an English mathematician and philosopher who worked extensively in many branches of pure mathematics and classical mechanics. Although he died young, he left a deep and long-lasting legacy, particularly in geometry. One of the main achievements that he is remembered for is his pioneering work on integrating Hamilton's Elements of Quaternions with Grassmann's Theory of Extension into a more general coherent corpus, now referred to eponymously as Clifford algebras. These geometric algebras are utilised in engineering mechanics (especially in robotics) as well as in mathematical physics (especially in quantum mechanics) for representing spatial relationships, motions, and dynamics within systems of particles and rigid bodies. Clifford's study of geometric algebras in both Euclidean and non-Euclidean spaces led to his invention of the biquaternion, now used as an efficient representation for twists and wrenches in the same context as that of Ball's Theory of Screws. Biographical NotesWilliam Kingdon Clifford was a 19th Century English mathematician and scientific philosopher who, though he lived a short life, produced major contributions in many areas of mathematics, mechanics, physics and philosophy. This he achieved during a mere fifteen-year professional career. He was the archetypal polymath, since as well as displaying remarkable mathematical skills, he was also an accomplished literature and classics scholar. Clifford was fluent in reading French, German and Spanish, as he considered these to be important for his mathematical work. He learned Greek, Arabic and Sanskrit for the challenge they presented, Egyptian hieroglyphics as an intellectual exercise, and Morse code and shorthand, because he wished to understand as many forms for communicating ideas as possible. During his lifetime Clifford was energetic and influential in championing the scientific method in

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Analyse und Synthese der Raumkurbelgetriebe mittels Raumliniengeometrie und dualer Größen

Cited by 10 publications

References 1 publication

The Dual Index and Dual Core Generalized Inverse

The Dual Index and Dual Core Generalized Inverse

The adjoint trigonometric representation of displacements and a closed‐form solution to the IKP of general 3C chains

William Kingdon Clifford (1845–1879)

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