Stiffness Modeling of the Tricept Robot Using the Overall Jacobian Matrix

Taking the 3DOF parallel mechanism within the Tricept robot as an example, this paper presents an analytical approach for the stiffness modeling of parallel kinematic machines having a properly constrained passive limb. The stiffness model is formulated using the 6×6overall Jacobian. It takes particular interest in the precise formulation of the bending stiffness matrix of the properly constrained passive limb by considering the compatibility conditions of the system. Stiffness evaluation of a sample Tricept robot is carried out using two global indices obtained from singular value decomposition of the compliance matrix.

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Posture, Workspace, and Manipulability of the Metamorphic Multifingered Hand With an Articulated Palm

Journal of Mechanisms and Robotics ◽

10.1115/1.4003414 ◽

2011 ◽

Vol 3 (2) ◽

Cited By ~ 29

Author(s):

Lei Cui ◽

Jian S. Dai

Keyword(s):

Jacobian Matrix ◽

Contact Point ◽

Gauss Map ◽

Singular Value ◽

Spherical Joint ◽

Additional Dimension ◽

Workspace Analysis ◽

Finger Motion ◽

Value Decomposition ◽

Relationship Of

This paper presents a novel multifingered hand with an articulated palm that makes the hand adaptable and reconfigurable. The posture of the new multifingered hand is enhanced by the additional motion of the palm and the workspace of fingers is augmented by the palm workspace. To analyze this integrated workspace, this paper introduces finger-operation planes to relate the finger motion to the palm motion and its configuration. Normals of these operation planes are used to construct a Gauss map. Adding an additional dimension, a four-dimensional ruled surface can be generated from this map to illustrate variation of posture. With the change of palm configurations, a posture manifold can be developed from the posture ruled surfaces. The workspace analysis is developed by introducing a palm workspace-triangle. This workspace-triangle evolves into a helical workspace-triangle tube when palm inputs vary and further develops into a four-dimensional presentation. This progresses into a set of workspaces of the multifingered hand by varying the palm configuration, leading to a larger workspace of the new multifingered hand as the union of the workspaces corresponding to individual palm configuration. This paper further investigates manipulability of the multifingered hand by modeling the contact point as a hypothetical spherical joint. Based on reciprocity relationship of screw systems, the finger Jacobian matrices and the hand Jacobian matrix are established. With singular value decomposition, manipulability of each finger is explored and the hand manipulability is revealed by the diagonal nature of the Jacobian matrix of the hand.

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Evaluation Method of Voltage Stability Based on Minimum Singular Value

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.511-512.1128 ◽

2014 ◽

Vol 511-512 ◽

pp. 1128-1132

Author(s):

Bing Liu ◽

Ying Wang ◽

Zhen Yang ◽

Yun Wei Li ◽

Hua Zhi Xie ◽

...

Keyword(s):

Singular Value Decomposition ◽

Limit Point ◽

Voltage Stability ◽

Evaluation Method ◽

Jacobian Matrix ◽

Stability Limit ◽

Singular Value ◽

Static Voltage Stability ◽

Stability Monitoring ◽

Value Decomposition

When the system reaches the static voltage stability limit point, Jacobian matrix is singular. By checking if minimum singular value is zero, its very easy to determine whether or not Jacobian matrix is singular. So the minimum singular value of Jacobian matrix can reflects the degree of system voltage stability effectively. Firstly this paper introduces singular value decomposition, analyses load characteristic and excitation limits involved in this method and examples on PSD-FDS are demonstrated. At last, suggestion on voltage stability monitoring by minimum singular value is proposed.

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On the Use of Metric-Dependent Methods in Robotics

Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2005-85445 ◽

2005 ◽

Cited By ~ 1

Author(s):

Dimiter Zlatanov ◽

Dragomir N. Nenchev

Keyword(s):

Singular Value Decomposition ◽

Jacobian Matrix ◽

Positive Definite ◽

Singular Value ◽

Generalized Inverses ◽

Scalar Products ◽

Value Decomposition

It is little known that the popular application of generalized inverses, singular value decomposition, conditioning numbers, and grasp and motion measures to many robotics problems involves the addition of different physical units. To redefine such techniques for proper use, meaningful screw scalar products must be used. The paper studies the use of both frame dependent positive-definite metrics and invariant, indefinite or degenerate, screw products for this purpose. Special attention is given to the diagonalization of the Jacobian matrix.

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