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rotational jacobian

Robotica (1)

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Kinematic analysis of limited-dof parallel manipulators based on translational/rotational Jacobian and Hessian matrices
Yi Lu, Yan Shi, Jianping Yu
Journal:

Robotica / Volume 27 / Issue 7 / December 2009

Published online by Cambridge University Press:

27 February 2009, pp. 971-980
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This paper proposes an approach for solving the velocity and acceleration of the limited-dof (dof n < 6) parallel kinematic machines with linear active legs by means of translational/rotational Jacobian and Hessian matrices. First, based on the established or derived constraint and displacement equations, the translational/rotational Jacobian and Hessian matrices are derived. Second, the formulae for solving inverse/forward velocities and accelerations are derived from translational and rotational Jacobian/Hessian matrices. Third, a 2SPR + UPU PKM and a 2SPS + RPRR PKM are illustrated for explaining how to use this method. This approach is simple because it needs neither to eliminate 6-n rows of an n × 6 Jacobian matrix nor to determine the screw or pose of the constrained wrench.