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Singularity-Free Trajectory Planning of a 3-RPRR Planar Kinematically Redundant Parallel Mechanism for Minimum Actuating Effort

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

Kinematic redundancy is a way to enlarge the workspace and to eliminate the singularities of parallel mechanisms. The objective of the present research is to introduce a new motion planning strategy for singularity avoidance and reducing the actuator forces, especially in the vicinity of singular configurations. The method is implemented to a planar kinematically redundant mechanism categorized as 3-RPRR type. Dynamic equations of motion are derived using the principle of virtual work, and the optimum inverse dynamics is obtained. Some numerical examples are solved, and the results are compared with those obtained in the counterpart non-redundant mechanisms. It is illustrated that the redundant mechanism can avoid singular configurations and track the given trajectory with feasible generalized forces.

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Abbreviations

a :

Dimension of the moving plate, Length of node pairs ppi (m)

b :

Length of node pairs OOi (m)

ℓ :

Length of the intermediate links (m)

\( {\mathbf{p}} \) :

Position vector of the center of the moving plate (m)

θ :

Orientation of the moving plate (rad)

θ i :

Angular position of the revolute actuators (rad)

d i :

Length of the prismatic actuators (m)

\( {\mathbf{A}}_{\theta } \) :

The rotation matrix from the moving plate to the reference frame

\( {\bar{\mathbf{u}}}_{p} \) :

Position vector of point, pi with respect to point p

\( {\mathbf{r}}_{pi} \) :

Position vector of point, pi

\( {\mathbf{r}}_{oi} \) :

Position vector of point, oi

\( {\mathbf{r}}_{bi} \) :

Position vector of point, bi

β i :

Orientation of the intermediate link (rad)

ω i :

Angular velocity of the intermediate links (rad/s)

α i :

Angular acceleration of the intermediate links (rad/s2)

\( {\mathbf{s}}_{i} \) :

Unit vector from point bi to pi

m p :

Mass of the moving plate (kg)

J p :

Inertia of the moving plate (kg m2)

J b :

Inertia of the prismatic actuators (kg m2)

F i :

Force of the ith prismatic actuator (N)

M i :

Moment of the ith revolute actuator (N m)

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Authors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, Shiraz, Iran

    Bahman Nouri Rahmat Abadi, M. Mahzoon & M. Farid

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  1. Bahman Nouri Rahmat Abadi
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  2. M. Mahzoon
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  3. M. Farid
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Correspondence to Bahman Nouri Rahmat Abadi.

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Nouri Rahmat Abadi, B., Mahzoon, M. & Farid, M. Singularity-Free Trajectory Planning of a 3-RPRR Planar Kinematically Redundant Parallel Mechanism for Minimum Actuating Effort. Iran J Sci Technol Trans Mech Eng 43, 739–751 (2019). https://doi.org/10.1007/s40997-018-0234-1

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  • DOI: https://doi.org/10.1007/s40997-018-0234-1

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