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Design Procedure for a Fast and Accurate Parallel Manipulator Sébastien Briot, Stéphane Caro, Coralie Germain

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Design Procedure for a Fast and Accurate Parallel Manipulator Sébastien Briot, Stéphane Caro, Coralie Germain Design Procedure for a Fast and Accurate Parallel Manipulator Sébastien Briot, Stéphane Caro, Coralie Germain To cite this version: Sébastien Briot, Stéphane Caro, Coralie Germain. Design Procedure for a Fast and Accurate Parallel Manipulator. Journal of Mechanisms and Robotics, American Society of Mechanical Engineers, 2017, 9 (6), pp.061012. 10.1115/1.4038009. hal-01587975 HAL Id: hal-01587975 https://hal.archives-ouvertes.fr/hal-01587975 Submitted on 13 Oct 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Design Procedure for a Fast and Accurate Parallel Manipulator Sebastien´ Briot∗ Stephane´ Caro CNRS CNRS Laboratoire des Sciences Laboratoire des Sciences du Numerique´ de Nantes (LS2N) du Numerique´ de Nantes (LS2N) UMR CNRS 6004 UMR CNRS 6004 44321 Nantes, France 44321 Nantes, France Email: [email protected] Email: [email protected] Coralie Germain Agrocampus Ouest 35042 Rennes, France Email: [email protected] printed circuit boards. This paper presents a design procedure for a two- Several robot architectures with four degrees of free- degree of freedom translational parallel manipulator, named dom (dof) and generating Schonflies¨ motions [2] for high- IRSBot-2. This design procedure aims at determining the speed operations have been proposed in the past decades [1, optimal design parameters of the IRSBot-2 such that the 3–6]. However, four dof robots are not always necessary, es- robot can reach a velocity equal to 6 m/s, an acceleration pecially for some simple operations requiring only two trans- up to 20 G and a multi-directional repeatability up to 20 µm lational dof in order to move a part from a working area throughout its operational workspace. Besides, contrary to to another. Therefore, several robot architectures provid- its counterparts, the stiffness of the IRSBot-2 should be very ing two translational dof motions have been synthesized in high along the normal to the plane of motion of its moving- the literature such as the five-bar mechanism [7,8], the para- platform. A semi-industrial prototype of the IRSBot-2 has placer [9] and several mechanisms with additional kinematic been realized based on the obtained optimum design param- chains used to constrain the platform rotations [6, 10, 11]. eters. This prototype and its main components are described It is noteworthy that the foregoing architectures are all in the paper. Its accuracy, repeatability, elasto-static per- planar, i.e., all their elements are constrained to move in the formance, dynamic performance and elasto-dynamic perfor- plane of motion. As a result, all their elements are subject mance have been measured and analyzed as well. It turns to bending effects along the normal to the plane of motion. out the IRSBot-2 has globally reached the prescribed spec- Therefore, in order for the mechanisms to be stiff enough ifications and is a good candidate to perform very fast and along this direction, their bodies are usually bulky, leading accurate pick-and-place operations. to high inertia and to low acceleration capacities. A two-dof spatial translational robot, named IRSBot-2, 1 Introduction IRSBot-2 standing for “IRCCyN Spatial Robot with 2 dof”, Parallel robots are more and more attractive for high- was introduced in [12]. It was shown that this robot archi- speed pick-and-place operations due to their lightweight ar- tecture may have better performance in terms of mass in mo- chitecture and high stiffness [1]. However, high velocities tion, stiffness and workspace size with respect to its serial and high accelerations may lead to some vibrations that may and parallel manipulator counterparts. The IRSBot-2 has a affect the robot accuracy and dynamic performance, thus dis- spatial architecture and the distal parts of its legs are not sub- carding those robots to be used as high-speed parallel robots ject to bending, but to tension, compression and torsion only. for special tasks requiring good accuracy and high accel- Consequently, its stiffness is increased and its total mass is erations such as the assembly of electronic components on reduced. In the same vein, the Par-2 robot composed of four legs was introduced in [13] as a mean to increase the stiffness of its mobile platform along the normal to its plane of mo- ∗Address all correspondence to this author. z0 Proximal l x 0 0 Base part P Motor k Parallelogram 0 Base z0 y0 y0 x0 y l l 0 2k x 1 Elbow 0 O y0 k l Motors 3k P k y11 k y0 y11 Distal k z21 k Leg II part z0 l 45° 41 k y11 k z22 k Platform l 42 k x0 Leg I P y11 k 2 Platform z 21 k l x 5k p P y Fig. 1. CAD modeling of the IRSBot-2. p x0 y0 z22 k tion. However, contrary to the Par-2 robot, the IRSBot-2 is composed of two legs only in order to reduce the mechanism Fig. 2. Kinematic chain of the kth leg (k = I; II). complexity and to increase its operational workspace size. This paper introduces a design procedure for the IRSBot-2 such that the multi-directional repeatability and the dynamic performance of the robot are optimum. A running Dk wPa prototype, which was built based on the obtained design pa- Base z0 P l1 rameters, is described too. Some experimental validations 0 b k A were performed and are analyzed in this paper. Note that this k qk O k Ck paper is an improved version of [14] with the following new x0 y0 x0 ex findings: Bk Tk ez v1 • on the multi-objective optimization problem (MOOP) E1k H for the design of the IRSBot-2: in [14], the three ob- k E2k jective functions were normalized and weighted in order P to convert the MOOP into a mono-objective optimiza- l2eq k Platform F1k v2 P z0 tion problem. Here, the Pareto-optimal solutions, i.e., 2 Gk l2 the non-dominated solutions, of the MOOP at hand are F2k presented. x0 y0 x0 y0 • on the experimental validations of the design method- P p ology: the IRSBot-2 semi-industrial prototype is de- Fig. 3. Parametrization of the kth leg (k = I; II). scribed and its deflection, repeatability and dynamic per- formance are analyzed experimentally. The paper is organized as follows. Section 2 presents The kth leg of the IRSBot-2 is shown in Fig. 2. It is the IRSBot-2 architecture and recalls its kinematic model- made of two modules: a proximal module and a distal mod- ing, which is described into detail in [15]. The design proce- ule (k = I; II). Therefore, the robot is made of a proximal dure developed for the determination of the optimal design part and a distal part shown in Fig. 1. The proximal part is parameters of the IRSBot-2 is introduced in Section 3. A composed of the base and the two proximal modules. The semi-industrial prototype of the IRSBot-2 and some experi- distal part is composed of the moving-platform and the two mental validations are described in Section 4. Finally, some distal modules. The base frame (O;x0;y0;z0) is attached to conclusions are drawn in Section 5. plane P0. The proximal module is a planar parallelogram, also named P joint, moving in the (O;x0;z0) plane and is com- 2 Kinematics of the IRSBot-2 posed of links `0k, `1k, `2k and `3k. The proximal module 2.1 Robot architecture keeps the angle between planes P0 and Pk equal to 45 deg. A CAD drawing of the IRSBot-2 architecture is shown The distal module is linked to body `3k of the parallel- in Fig. 1. The IRSBot-2 is a two-dof translational parallel ogram through two universal joints at points E jk. The first manipulator. Its kinematic architecture is composed of two axis of the universal joints y11k is located in planes Pk and spatial limbs with identical joint arrangements. (x0 E jk y0). Moreover, the distal module is also linked to the prox1 which is made of an I-shape beam leading to a better th behavior when faced with bending effects (Fig. 4). th Φ In order to reduce the number of design variables and to ov L z oprox 1 simplify the design problem the beams are supposed to have the same thickness th. Similarly, the height and width of the I-shape beams are the same and equal to Loprox1. Moreover, 2 the moving platform is considered as rigid. v = prox , elb, dist Loprox 1 As a consequence, the design parameters of the IRSBot- Fig. 4. Beam cross-section parameters 2 are classified as follows: Lengths: l1, l2 (or l2eq), b, p, wPa, ex, ez, v1 and v2; Angles : ak; body ` of the moving platform through two universal joints 5k Cross-section parameters : fon, Loprox1, th. located at points Fjk ( j = 1;2). Axes z21k and z22k are sym- Additionnally, one must consider the material parame- metrical with respect to plane (x0 Oz0). Links `41k and `42k are not parallel. This configuration prevents the distal mod- ters (Young and shear moduli, material density) that are as- ule from becoming a spatial parallelogram and the robot ar- sumed to have a known constant value.
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