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Inverse dynamics of the HALF parallel manipulator with revolute actuators

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Abstract

Recursive matrix relations for kinematics and dynamics of the HALF parallel manipulator are presented in this paper. The prototype of this robot is a spatial mechanism with revolute actuators, which has two translation degrees of freedom and one rotation degree of freedom. The parallel manipulator consists of a base plate, a movable platform and a system of three connecting legs, having wide application in the fields of industrial robots, simulators, parallel machine tools and any other manipulating devices where high mobility is required. Supposing that the position and the motion of the moving platform are known, an inverse dynamics problem is solved using the principle of virtual powers. Finally, some iterative matrix relations and graphs of the torques and powers for all actuators are analysed and determined. It is shown that this approach is an effective means for kinematics and dynamics modelling of parallel mechanisms.

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Abbreviations

a k,k−1 :

& orthogonal transformation matrix

a=Q T :

General transformation matrix of moving platform

⇁ u1 ,⇁ u2 ,⇁ u3 :

three orthogonal unit vectors

α:

angle of initial inclination of upper arm of three legs

ϕ k,k−1 :

relative rotation angle of T k rigid body

⇁ ω k,k - 1 :

relative angular velocity of T k

⇁ ω k0 :

absolute angular velocity of T k

~ω k,k - 1 :

skew-symmetric matrix associated to the angular velocity ⇁ ω k,k - 1

⇁ ε k,k - 1 :

relative angular acceleration of T k

⇁ ε k0 :

absolute angular acceleration of T k

~ε k,k - 1 :

skew-symmetric matrix associated to the angular acceleration ⇁ ε k,k - 1 $

⇁ rk,k - 1 A :

relative position vector of the centre of A k joint

⇁ vk,k - 1 A :

relative velocity of the centre A k

⇁ γ k,k - 1 A :

relative acceleration of the centre A k

m k :

mass of T k rigid body

Ĵk :

symmetric matrix of tensor of inertia of T k about the link-frame A kxkykzk

J 1, J 2 :

two Jacobian matrices of the manipulator

m A 10, m B 10, m C 10 :

torques of three actuators pointing about the A 1 z A 1, B 1 z B 1, C 1 z C 1 directions

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Authors and Affiliations

  1. Department of Mechanics, University “Politehnica” of Bucharest, Bucharest, Romania

    Stefan Staicu

  2. Department of Precision Instruments, Institute of Manufacturing Engineering, Tsinghua University, Beijing, 100084, P.R. China

    Xin-Jun Liu & Jinsong Wang

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  1. Stefan Staicu
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  2. Xin-Jun Liu
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  3. Jinsong Wang
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Correspondence to Xin-Jun Liu.

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Staicu, S., Liu, XJ. & Wang, J. Inverse dynamics of the HALF parallel manipulator with revolute actuators. Nonlinear Dyn 50, 1–12 (2007). https://doi.org/10.1007/s11071-006-9138-5

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