Mobility and spatiality of parallel robots revisited via theory of linear transformations

• Published in: European journal of mechanics, A, Solids Vol. 24; no. 4; pp. 690 - 711
• Main Author: Gogu, Grigore
• Format: Journal Article
• Language: English
• Published: Paris Elsevier Masson SAS 01.07.2005; Elsevier
• Subjects: Applied sciences; Drives; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Linear transformations; Linkage mechanisms, cams; Mechanical engineering. Machine design; Mobility; Parallel robots; Physics; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Spatiality; Mobility; Linear transformations; Parallel robots; Spatiality; Closed loop; Machining; Parallel mechanism; Modeling; Robotics; Parallel robots: Mobility; Linear transformation; Kinematics; Linkage mechanism; Open loop; Kinematic chain
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2005.02.004

Parallel robots are extensively used for various applications including manipulation, machining, guiding, testing and control. The mechanical architecture of parallel robots is based on parallel mechanisms in which a mobile platform is connected to a reference element by at least two legs. Mobility and spatiality are the main structural and kinematic parameters of a parallel robot. These two parameters are defined via the theory of linear transformation and can be easily determined by inspection using the definitions, properties and theorems introduced in this paper. An analytical method to compute these parameters is also presented just for verification and for a better understanding of their meanings. The new formalism presented in this paper is based on spatiality of an elementary open kinematic chain and relative spatiality between two elements of a closed kinematic chain. As far as we are aware, this paper demonstrates for the first time a new formula for calculation of general (full-cycle) mobility of parallel robots that overcomes the drawbacks of Chebychev–Grübler–Kutzbach's mobility criterion largely used for mobility calculation of multi-loop mechanisms. This new formula is easily applicable to parallel robotic manipulators with elementary or complex legs and mobility calculation does not involve the setting up of instantaneous constraint systems associated to the parallel mechanism.