Mobility and spatiality of parallel robots revisited via theory of linear transformations
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...
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| Published in | European journal of mechanics, A, Solids Vol. 24; no. 4; pp. 690 - 711 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Paris
Elsevier Masson SAS
01.07.2005
Elsevier |
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| Abstract | 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. |
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| AbstractList | 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. 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 (fullcycle) mobility of parallel robots that overcomes the drawbacks of Chebychev-Griibler-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. In a parallel mechanism the mobile platform is in-parallel connected to the reference element (also called reference platform) by at least two legs that can be elementary or complex. Parallel mechanisms are extensively used today in parallel robotic manipulators whose industrial and economic relevance is continuously growing. This technology can be considered a well-established option for many different applications of manipulation, machining, guiding, testing, control, etc. Parallel mechanisms have been the subject of study of much robotic research during the last two decades (Merlet, 1990, 1997; Tsai, 2000). Mobility and spatiality are the main structural parameters of a mechanism and represent the first considerations in kinematic and dynamic studies of a multi-body system. Mechanism mobility indicates the number of independent joint parameters required to determine the position of a point situated on any element of the mechanism. Spatiality indicates the independent relative |
| Author | Gogu, Grigore |
| Author_xml | – sequence: 1 givenname: Grigore surname: Gogu fullname: Gogu, Grigore email: Grigore.Gogu@ifma.fr organization: Mechanical Engineering Research Group, French Institute of Advanced Mechanics and University Blaise Pascal, campus de Clermont-Ferrand/les Cezeaux, BP 265, 63175 Aubière, France |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Mobility and spatiality of parallel robots revisited via theory of linear transformations |
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