Derivation of dual forces in robot manipulators

Brodsky, V.; Shoham, Moshe

doi:10.1016/s0094-114x(97)00089-x

Cited by 11 publications

(2 citation statements)

References 3 publications

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“…where Brodsky and Shoham treat objects as a set of discrete mass elements, each of which corresponds to a unique velocity spinor ω = ω + εv [26,27]. The dual mass of the mass element is described as d m = dmd/dε, The linear momentum d m ω = dm d dε (ω + εv) = vdm of each mass element is the product of the dual mass and the velocity spin.…”

Section: Mathematical Model Of a Single Rigid-flexion Coupled Spacecraftmentioning

confidence: 99%

Rigid–Flexible Coupled System Attitude–Orbit Integration Fixed-Time Control

Zhang

et al. 2023

Electronics

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A diffractive imaging system consisting of two satellites is analyzed in view of dynamics. The mathematical model of rigid and flexion couples is studied to describe the relative motion of diffractive satellites and imaging satellites. Based on an integrated dynamics model with dual quaternion, a fixed-time non-singular terminal sliding mode controller is designed to meet the requirements of Earth observation. Finally, introducing the non-singular terminal sliding mode as the control group, a comparative simulation of relative motion and control is implemented to verify the controller and dynamics model.

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Section: Mathematical Model Of a Single Rigid-flexion Coupled Spacecraftmentioning

confidence: 99%

Rigid–Flexible Coupled System Attitude–Orbit Integration Fixed-Time Control

Zhang

et al. 2023

Electronics

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“…Dual matrices are used in many fields today. In Kinematics, for example, with the aid of the principle of transference [2], many problems can be initially stated under the condition of spherical motion and then extended to spiral motion after the dualization of the equation, which makes the dual matrix widely used in space agency kinematics analysis and synthesis [3,4,5,6] and robotics [7,8,9,10,11]. 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].…”

Section: Introductionmentioning

confidence: 99%

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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Dynamics of serial chain systems using dual algebra

Dan

Saha

2022

Multibody Syst Dyn

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Derivation of dual forces in robot manipulators

Cited by 11 publications

References 3 publications

Rigid–Flexible Coupled System Attitude–Orbit Integration Fixed-Time Control

Rigid–Flexible Coupled System Attitude–Orbit Integration Fixed-Time Control

The Dual Index and Dual Core Generalized Inverse

Dynamics of serial chain systems using dual algebra

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