Derivation of General Acceleration and Hessian Matrix of Kinematic Limbs in Parallel Manipulator by Extended Skew-Symmetric Matrixes

Lü, Yi; Ye, Nijia; Chang, Zefeng

doi:10.1007/s11831-020-09490-6

Cited by 7 publications

(8 citation statements)

References 23 publications

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“…Let C be a three layers 3 × 3 constant matrix. Let I k (k = 1, 2, 3) be the 3 × 3 sub-matrixes of C. The relative formulas are represented by [21].…”

Section: Kinematics Model Of Moving Platformmentioning

confidence: 99%

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Development and dynamics of a novel couple-constrained parallel wrist with three measuring force flexible fingers

Chang

Lü

2023

Robotica

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A novel couple-constrained parallel wrist with three measuring force flexible fingers is designed for grabbing heavy objects and measuring grabbed forces. Its prototype is developed, its dynamics model is established, and its grabbing forces are measured. First, using the extended formulas of the skew-symmetric matrix, the kinematic formulas are derived for solving the Jacobian/Hessian matrices and the general velocity/acceleration of the moving links in the couple-constrained parallel wrist. Second, a dynamics model is established for solving the dynamic actuation forces, the couple-constrained forces, and the torque in the couple-constrained parallel wrist. Third, the theoretical solutions of the kinematics/dynamics of the couple-constrained parallel wrist are verified using a simulation mechanism. Finally, the grabbing forces of the three flexible fingers are measured and analyzed.

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“…Let C be a three layers 3 × 3 constant matrix. Let I k (k = 1, 2, 3) be the 3 × 3 sub-matrixes of C. The relative formulas are represented by [21].…”

Section: Kinematics Model Of Moving Platformmentioning

confidence: 99%

“…Let I k ( k = 1, 2, 3) be the 3 × 3 sub-matrixes of C . The relative formulas are represented by [21].…”

Section: Kinematics Of Couple-constrained Parallel Wrist With Three M...mentioning

confidence: 99%

Development and dynamics of a novel couple-constrained parallel wrist with three measuring force flexible fingers

Chang

Lü

2023

Robotica

Self Cite

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“…The differentiation items −P ′ o and − P′ o are derived from equations (11) and (31) and Ref. 31 as follows:…”

Section: Velocity and Acceleration Of Grasped Moving-object In {B}mentioning

confidence: 99%

“…Differentiation of J r in equation ( 32) and its first item J ′ Po J −1 B m T ′tj J o are derived from equation (33) and Ref. 31 as follows:…”

Section: Velocity and Acceleration Of Grasped Moving-object In {B}mentioning

confidence: 99%

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Dynamics of moving-object grasped by a hybrid hand

Chang

2021

Proceedings of the Institution of Mechanical Engineers, Part K:

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When a heavy object is cooperatively grasped to move by several fingers of the robot hybrid hand, the inertial properties and the mass distribution of the object must influence largely on the operation precision, grasping stability, and the safety of both the hybrid hand and the object. Hence, it is an important and significant issue to establish and analyze the dynamics model of the moving-object cooperatively grasped by the hybrid hand in order to ensure the safety and grasping stability of the hybrid hand and the object. However, this research has not been conducted. In this paper, a dynamics model of the moving-object grasped by the hybrid hand is established, and its dynamics is studied and analyzed. First, a three-dimensional model of a hybrid hand formed by a novel parallel manipulator and three fingers is designed for cooperatively grasping object. Second, the kinematic formulas for solving the Jacobian matrices, the Hessian matrices, the general velocity/acceleration of the moving platform, and four active limbs of the parallel manipulator are derived. Third, the composite Jacobian matrix and the composite Hessian matrix of the hybrid hand are derived, and the general velocity/acceleration of the moving-object grasped by the hybrid hand is derived. Fourth, dynamics model of the hybrid hand is established, the formulas for solving the dynamic actuation forces of the three fingers and the dynamic actuation forces/torque and constrained forces of the parallel manipulator are derived. Finally, the theoretical solutions of the dynamics model of the moving-object grasped by the hybrid hand are verified by its simulation mechanism.

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Improved inverse kinematics and dynamics model research of general parallel mechanisms

Zhang

Wang

et al. 2023

J Mech Sci Technol

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Derivation of General Acceleration and Hessian Matrix of Kinematic Limbs in Parallel Manipulator by Extended Skew-Symmetric Matrixes

Cited by 7 publications

References 23 publications

Development and dynamics of a novel couple-constrained parallel wrist with three measuring force flexible fingers

Development and dynamics of a novel couple-constrained parallel wrist with three measuring force flexible fingers

Dynamics of moving-object grasped by a hybrid hand

Improved inverse kinematics and dynamics model research of general parallel mechanisms

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