fulltext02 - Multibody Syst Dyn (2010) 23: 5775 DOI...

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Multibody Syst Dyn (2010) 23: 57–75 DOI 10.1007/s11044-009-9174-2 A new family of constrained redundant parallel manipulators J. Gallardo-Alvarado · G. Alici · L. Pérez-González Received: 10 January 2008 / Accepted: 13 August 2009 / Published online: 30 September 2009 © Springer Science+Business Media B.V. 2009 Abstract This paper addresses the description and kinematic analysis of a new family of redundant parallel manipulators. The primary feature of the new family is to have a compact topology consisting of multi-degree of freedom non-identical limbs. In order to simplify the forward position analysis, the motion of the end-effector (platform) is decoupled into translational and rotational components with respect to the base. This kind of topology is in agreement with the parallel manipulator deFnition of I±ToMM—a parallel manipulator ...thatcontrolsthemotionofitsend-effectorbymeansofatleasttwokinematicchainsgo- ing from the end effector towards the frame. . . ”. In fact, adding a kinematic pair to a limb of a non-redundant parallel manipulator creates asymmetrical parallel manipulator. Analytical expressions for the forward position, velocity, and acceleration of the parallel manipulators have been obtained and solved for an exemplary 7-DO± redundant parallel manipulator. The numerical results from the analytical expressions are veriFed by comparing them to the re- sults from a mechanical system simulation software as if a real parallel manipulator is being run to collect the position, velocity, and acceleration data. ±inally, based on the velocity formulation, the singularity analysis of the manipulator is also provided. Keywords Redundant parallel manipulator · Decoupled motion · Closed-form solution · Klein form · Screw theory · Kinematics 1 Introduction Parallel manipulators which consist of at least two limbs have many advantages such as high accuracy in positioning due to non-accumulation of link errors, high speed movements, and J. Gallardo-Alvarado ( B ) · L. Pérez-González Department of Mechanical Engineering, Instituto Tecnológico de Celaya, Av. Tecnológico y A. García Cubas, 38010 Celaya, Gto., Mexico e-mail: [email protected] G. Alici School of Mechanical, Materials, and Mechatronic Engineering, University of Wollongong, Wollongong, NSW, Australia e-mail: [email protected]
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58 J. Gallardo-Alvarado et al. a high load-carrying capacity due to sharing an external load among their limbs. On the other hand, their main disadvantage is a limited workspace and maneuverability due to the existence of singularities within their workspace, and their compact topology. Although the redundancy concept has been widely studied for serial manipulators [ 1 7 ], its beneFts to cir- cumvent the disadvantages of parallel manipulators have not been fully investigated. A re- dundant parallel manipulator can be physically realized in three ways [ 8 ]; (i) adding at least one more equivalent limb to the existing non-redundant topology, (ii) increasing the number of active joints in any limb such that the number of active joints is higher than needed, and
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fulltext02 - Multibody Syst Dyn (2010) 23: 5775 DOI...

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