Dynamics of Kinematic Chains

Stokes, A.; Brockett, Roger W.

doi:10.1177/027836499601500406

Cited by 15 publications

(3 citation statements)

References 9 publications

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“…Blajer et al (1994) have also presented an orthogonal complement based formulation for the constrained multibody systems. Park et al (1995) presented robot dynamics using a Lie group formulation, while Stokes and Brockett (1996) derived the equations of the motion of a kinematic chain using concepts associated with the special Euclidean group. McPhee (1996) showed how to use linear graph theory in multibody system dynamics.…”

Section: Introductionmentioning

confidence: 99%

Evolution of the DeNOC-based dynamic modelling for multibody systems

2013

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Abstract. Dynamic modelling of a multibody system plays very essential role in its analyses. As a result, several methods for dynamic modelling have evolved over the years that allow one to analyse multibody systems in a very efficient manner. One such method of dynamic modelling is based on the concept of the Decoupled Natural Orthogonal Complement (DeNOC) matrices. The DeNOC-based methodology for dynamics modelling, since its introduction in 1995, has been applied to a variety of multibody systems such as serial, parallel, general closed-loop, flexible, legged, cam-follower, and space robots. The methodology has also proven useful for modelling of proteins and hyper-degree-of-freedom systems like ropes, chains, etc. This paper captures the evolution of the DeNOC-based dynamic modelling applied to different type of systems, and its benefits over other existing methodologies. It is shown that the DeNOC-based modelling provides deeper understanding of the dynamics of a multibody system. The power of the DeNOC-based modelling has been illustrated using several numerical examples.

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Section: Introductionmentioning

confidence: 99%

Evolution of the DeNOC-based dynamic modelling for multibody systems

2013

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“…This idea seem to date back to Asada & Youcef-Toumi (1986) but was also studied by Stokes & Brockett (1996). The advantage of this scheme is that the tensor C ijk will disappear from the equations of motion since it is essentially a matrix of derivatives of the entries of the mass matrix.…”

Section: Constant Mass Matrix For Serial Robotsmentioning

confidence: 99%

Equimomental Systems and Robot Dynamics

Selig¹

2015

Proceedings of the IMA Conference on Mathematics of Robotics

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Three different concepts from the past are reviewed from a more modern standpoint. Constructing an equimomental system of four point-masses to an arbitrary rigid-body; the conditions for the generalised mass matrix of a serial robot to be constant and how to dynamically balance an arbitrary rigid body so that it is symmetrical about a given axis. Connections are made to the geometry of a 3-dimensional Veronese variety.

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“…are considered for the selection of a robot. Dynamics is generally neglected at this stage, even though it is widely used for control [7][8][9][10][11][12] and simulation of robots [12][13][14][15][16][17]. In this paper, simplicity of dynamic model and its computations are emphasized, particularly, with respect to the generalized inertia matrix (GIM), which has been proposed as a criterion for robot architecture selection.…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Model Based Robot Arm Selection Criterion

Bhangale

Saha

Agrawal

2004

Multibody System Dynamics

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Abstract. The selection of robot manipulator architecture, i.e. the determination of link lengths, their relative orientations, types of joints, e.g. revolute or prismatic, etc., has been largely done so far by experience, intuition and at most based on the kinematic considerations like workspace, manipulability, etc. Dynamics is generally ignored at this stage even though it is widely used for control and simulation. This paper attempts to introduce a criterion based on the dynamics of a robot manipulator, namely, simplicity of the associated generalized inertia matrix (GIM). Since the GIM influences both the control and simulation algorithms significantly, its fast computation and / or making its shape diagonal will certainly enhance the speed, precision, and stability of the robots. Two measures of simplicity, the computation complexity of the GIM in terms of floating point operations and the computer CPU time of an algorithm where the GIM appears, e.g., the inverse dynamics algorithm, are used here to evaluate a robot arm. The proposed criterion is illustrated with two -link robot arms with revolute and prismatic joints and compared with the two commonly used criteria, namely, the workspace, and manipulability. Finally, an example is taken to select an arm from the two spatial robot architectures, RTX and Stanford.

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Dynamics of Kinematic Chains

Cited by 15 publications

References 9 publications

Evolution of the DeNOC-based dynamic modelling for multibody systems

Evolution of the DeNOC-based dynamic modelling for multibody systems

Equimomental Systems and Robot Dynamics

A Dynamic Model Based Robot Arm Selection Criterion

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