Design and Analyses of a Macro Parallel Robot with Flexure Hinges for Micro Assembly Tasks

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1 Design and Analyses of a Macro Parallel Robot with Flexure Hinges for Micro Assembly Tasks J. Hesselbach, A. Raatz, J. Wrege, S. Soetebier Institute of Machine Tools and Production Technology IWF Technical University of Braunschweig, Germany Abstract In this paper a macro parallel robot is presented in which conventional bearings are replaced by pseudo-elastic flexure hinges. The robot consists of a spatial parallel structure with three translational degrees of freedom and is driven by three linear direct drives. The structure has been optimised with respect to workspace and transmission ratio. Additionally, in simulations with the FEM tool ANSYS different geometrical arrangements and combinations of flexure hinges have been investigated with respect to the dynamic behaviour of the compliant mechanism. The main frequencies are in the range of 120 Hz and due to the symmetrical character of the structure the vibrations of the compliant mechanism should be damped quite fast. Keywords: compliant mechanism, parallel structure, flexure hinges, pseudo-elastic SMA, high precision assembly 1 INTRODUCTION Because of improvements in microsystem technology, making complex hybrid microsystems possible which require some kind of assembly, new handling technologies have to be developed. As an alternative to conventional serial robots for handling and positioning tasks parallel robots can be used. Due to the structure parallel robots have advantages with respect to speed and positioning accuracy. Detailed discussion concerning properties of parallel mechanisms can be found in [1]. A typical problem of parallel structures is the high number of joints and joints with more than one degree of freedom which may result in a decreasing precision because of their backlash, friction and slip-stick-effects. In high precision assembly tasks in microsystem technology these problems have been overcome by using flexure hinges instead of conventional rotational joints, e.g. [2-5]. The integration of flexure hinges in parallel structures is especially simple, because except of the drives all joints are passive. Since flexure hinges gain their mobility exclusively by the elastic deformation of matter, they do not posses the above named disadvantages. But for the same reason their attainable angle of rotation is strongly limited when using conventional metallic materials with approximately 0.5% maximal elastic strains or plastics with approximately 1% elastic strains. Due to this flexure hinges are mainly used in small devices like micropositioning devices, micro-grippers with small angular deflections and limited workspaces. In this approach a macro parallel robot is investigated in which the conventional bearings are to be replaced by pseudo-elastic flexure hinges. The material of the flexure hinges is a shape memory alloy (SMA) which offers elastic strains up to 17%. Depending on the geometry of the hinges the maximal angular deflection angles differs, but for the construction of the compliant mechanism ± 30 degrees are assumed. This offers the possibility to design a robot with a sufficiently large workspace for typical micro assembly tasks. 2 PSEUDO-ELASTIC FLEXURE HINGES A wide variety of different designs of flexure hinges are known [6, 7]. In most cases it is tried to achieve high angular deflections with small occurring elastic strains. Plastic deformations should be avoided due to decreasing numbers of possible load cycles caused by induced defects in the material. Figure 1: Stress-strain diagram of pseudo-elastic SMA 1

2 Pseudo-elastic shape memory materials gain their reversible strains not only by a distortion of the atomic lattice [8]. Figure 1 shows exemplarily a uniaxial stressstrain diagram of a pseudo-elastic SMA. Shape memory alloy exists in at least two different phases (austenite and martensite) depending on the temperature or the applied stress. Initially a pseudo-elastic material is in its austenitic phase. In the beginning when loaded its deformations are elastic, in a conventional meaning. When further loaded a transformation from the austenitic phase to the martensitic phase is induced. This transformation is accompanied with large reversible strains at nearly constant stresses. When unloaded a retransformation form martensite into austenite occurs at lower stresses resulting in a stress hysteresis. In our case we use a single crystal CuAlNi alloy with two stress plateaus and maximal reversible strains up to 17%. Since the material is by now only available in rods the design of the flexure hinges is quite restricted. Figure 2 shows the chosen geometrical dimensions of the used flexure hinge with one degree of freedom (DOF). R=15mm 3mm 3 STRUCTURE OF THE PARALLEL ROBOT (TRIGLIDE S ) In the following section a short description of the structure of the chosen parallel robot is given (Figure 3) [11]. The structure is a variant of the Delta robot of Clavel [12] and the Star robot of Hervé [13]. The robot consists of a spatial parallel structure with three translational degrees of freedom and is driven by three linear actuators. The platform is connected with each drive by two links forming a parallelogram and allowing only translational movements of the platform and keeping the platform parallel to the base plane. An additional rotational axis can be mounted on the working platform to adjust the orientation of the end-effector. y M q i x axis of rotation 0,15mm x-axis secondary axis z Figure 2: Flexure hinge with 1 DOF In order to gain high numbers of life cycles we are restricting the maximal occurring strains about 4.2% at deflections of 30. Investigations of the kinematic behaviour of flexure hinges show that there are deviations between flexure hinges and ideal rotational joints. These deviations are caused by the movements of the instantaneous centre of rotation during deflection. The deviations are also reflected in the kinematic behaviour of the robot with integrated flexure hinges (compliant mechanism) [9]. The error which is induced when describing the compliant mechanism by means of a rigid body model does influence the absolute positioning accuracy but not the resolution and the repeatability. With two other designed compliant robots it could be shown that the error is only small and negligible if only a good repeatability and resolution is needed for the assembly task [10]. α TCP Figure 3: Structure of the parallel robot (Triglide) The three drives of the structure are arranged in the base plane at intervals of 120 degrees star-shaped. Thus the structure has a workspace which is nearly round or triangle-shaped. By restricting the angular deflection of the flexure hinges the workspace is reduced and also changes slightly its shape. Figure 4 shows the workspace of the structure if there is no restriction of the angular deflection (a, b) and with a restriction of deflection of ± 20 (c, d) p 2

spatial view Table 1 gives the results of this workspace optimisation.

with no angular restriction. The workspace reaches its maximum in the plane with z = 195 mm.

top view (c) spatial view y [mm] min, max z [mm] min, max work space ± 180-218,176-206,206-324,0 1 ±

45 Table 1: Workspace dimensions of the structure With a design angle of α0 = 34 (Figure 3) the workspace of the

The angle α0 is the angle between the planes of the parallelograms and the working platform in the initial

x z x [mm] min, max (d) top view Figure 4: Workspace of the structure with no restrictions of angular deflections

view (c) (d) Figure 5: Optimised workspace of the compliant robot (Triglides) Due to the symmetric structure and

3 spatial view Table 1 gives the results of this workspace optimisation. The displacement of the drives is restricted to q = 315 mm and the geometrical dimensions are chosen to M = 350 mm and p = 45 mm. The restriction of the hinges deflections of ± 30 reduces the workspace only minimal compared to the workspace with no angular restriction. The workspace reaches its maximum in the plane with z = 195 mm. The shape is roughly a circle with a diameter of 300 mm. top view (c) spatial view y [mm] min, max z [mm] min, max work space ± , , ,0 1 ± , , , ± , , , Table 1: Workspace dimensions of the structure With a design angle of α0 = 34 (Figure 3) the workspace of the structure is optimized when the deflection angle of the flexure hinges is restricted to ± 30 (Figure 5). The angle α0 is the angle between the planes of the parallelograms and the working platform in the initial position of the structure with no deflections of the hinges. x z x [mm] min, max (d) top view Figure 4: Workspace of the structure with no restrictions of angular deflections (± 180, a, b) of the flexure hinges and with a restriction of ± 20 (c, d) y deflection (c) (d) spatial view top view (c) (d) Figure 5: Optimised workspace of the compliant robot (Triglides) Due to the symmetric structure and the chosen length of the legs a homogeneous transmission behaviour from the drives to the working platform is obtained. Figure 6 shows exemplarily the ratio t platform movement in the plane r to drive movement q at two different zcoordinates. t= r = q x 2 + y 2 q (1) It can also be well seen that the shape of the workspace in a plane depends on the position of this plane in zdirection. At z = 100 mm the ratio ranges from 1.3 in the middle to 1.6 at the edge; at z = 200 mm from 1.02 to 0.82, respectively. The transmission ratio gets better the larger z is but at the same the workspace in the plane gets smaller. The dimensions of the structure are calculated in a way that the transmission ratio t from platform to drive is smaller than 1 within the used workspace (190 mm < z < 250 mm). Theoretically this enables a more accurate positioning of the platform than the drives themselves z = 100 mm z = 200 mm 3

The results of the modal analysis for two design variants are given in Table 2. Due to symmetry groups of frequencies can be defined for which the deformation mode is similar. 0.97 0.74 0.85 0.

7 (d) z = 300 mm secondary axes Figure 6: Transmission ratio of the structure in different planes 4 COMPLIANT MECHANISM platform One problem of flexure hinges and compliant mechanism is that the

In various simulations with the FEM tool ANSYS different geometrical arrangements and combinations of flexure hinges have been investigated with respect to the dynamic behaviour (natural frequencies

The spatial parallelogram of the structure is built with one, connected to the platform and the drives, respectively, and two secondary axes, at which the parallelogram rods are connected.

4 The results of the modal analysis for two design variants are given in Table 2. Due to symmetry groups of frequencies can be defined for which the deformation mode is similar (c) z = 250 mm (d) z = 300 mm secondary axes Figure 6: Transmission ratio of the structure in different planes 4 COMPLIANT MECHANISM platform One problem of flexure hinges and compliant mechanism is that the hinges act as springs with restoring forces. Without any damping component, except for the inner material damping, the compliant mechanism normally tends to vibrate due to the compliance. In various simulations with the FEM tool ANSYS different geometrical arrangements and combinations of flexure hinges have been investigated with respect to the dynamic behaviour (natural frequencies and forms) of the compliant mechanism. Figure 8 and 9 show two different possibilities to design the structure. The spatial parallelogram of the structure is built with one, connected to the platform and the drives, respectively, and two secondary axes, at which the parallelogram rods are connected. The primary and the secondary axes must intersect to allow for two degrees of freedom. The flexure hinges with one degree of freedom (Figure 1) has to be combined in such a way offering two degrees of freedom with intersecting rotational axes (Figure 7). Figure 8: Design of the combined flexure hinge (2 DOF) with outer (o-pa design) Figure 9: Design of the combined flexure hinge (2 DOF) with inner (i-pa design) secondary axis 1 secondary axis 2 Design model Mode number Frequenc y [Hz] pa-bending / outer primary Figure 7: Rotational axes of the flexure hinges and axes of the spatial parallelogram of the structure Deformation mode 1, ,4, ,7, pa-bending 10, pa-bending, sa-bending sa-bending 13,14, sa-bending axis 4

innerprimary axis 16,17 158.3 pa-bending, sa-bending 18 166.2 pa-bending 19,20 191.2 pa-bending, sa-bending 21,22,23 203.2 206.9 pa-bending, sa-bending, 24 218 pa-bending, sa-bending 25 235.

2 sa-bending 11,12,13 131.8 sa-bending 14,15 151,6 sa-bending 167.6 sa- 16-21 174.8 22 183.5 sa- 23,24 194.5 sa-, sa-bending 25,26,27 217.

minimise the moved mass which is 1120 g (Figure 11 and 12). The robot is driven by linear direct drives with an incremental measuring system with a resolution of 0.1 micrometer.

5 innerprimary axis 16, pa-bending, sa-bending pa-bending 19, pa-bending, sa-bending 21,22, pa-bending, sa-bending, pa-bending, sa-bending pa-bending, sa-bending, sa-bending 1, pa-bending, sa pa-, sa- bending 4,5, pa-, sa- bending 7, sa-bending, sa pa-bending sa-bending 11,12, sa-bending 14,15 151,6 sa-bending sa sa- 23, sa-, sa-bending 25,26, sa-bending 28,29, combination secondary axes Figure 10: Final design of combined flexure hinges The compliant robot consists of 84 discrete flexure hinges and is built with CFK rods to minimise the moved mass which is 1120 g (Figure 11 and 12). The robot is driven by linear direct drives with an incremental measuring system with a resolution of 0.1 micrometer. Table 2: Results of modal analyses of two design variants of the compliant mechanism (FEM tool ANSYS) With additional spectrum analyses and transient analyses the frequencies of the structures could be determined which have the largest influence (see marked in Table 2). In both cases the mode number 9 with 125 Hz and 118 Hz, respectively, are the dominant frequencies. Though the o-pa design seems to be a bit stiffer for the final robot design the design variant with inner was chosen due to the possibility of more compact design. Figure 10 shows the combination of flexure hinges. Due to parallel and angular arrangement of the hinges the al moments should be better absorbed and transformed into tension and compression forces. Figure 11: Compliant macro parallel robot (Triglide s ) secondary axis 1 secondary axis 2 Figure 12: Working platform (view from bottom) 5

6 Due to symmetrical arrangement of the structure with respect to the support of the working platform and optimised combinations of flexure hinges a quite rigid structure was built and occurring vibrations will be damped quite fast. 5 SUMMARY This paper presents the design of a spatial compliant parallel robot with pseudo-elastic flexure hinges. The robot has three degrees of freedom and a workspace larger than 200 x 200 x 60 mm³. The compliant mechanism has been optimised with respect to workspace, transmission ratio and stiffness. Due to the lack of backlash, friction and stick-slip effects within the mechanism the repeatability and resolution should be better than 1 µm and 0.1 µm, respectively. In following experiments the accuracy and the dynamic behaviour will be investigated. Assembly", Production Engineering, Vol. IX/1, pp , [12] Clavel R.: DELTA, a fast robot with parallel geometry, 18th Int. Symp. on Industrial Robot, pp , [13] Hervé, J. M. and Sparacino, F.: Star, a new concept in robotics, Proc. 3rd Int. Workshop on ARK, Ferrara, Italy, pp , REFERENCES [1] Merlet, J.P.: Les robots parallèles, Édition Hermes, Paris, [2] Canfield, S. L., Beard, J. W., Lobontiu, N., O'Malley, E., Samuelson, M., and Paine, J., "Development of a spatial compliant manipulator", International Journal of Robotics and Automation, vol. 17, no. 1, pp , [3] Pernette, E., Henein, S., Magnani, I., and Clavel, R., "Design of parallel robots in microrobotics," Robotica, vol. 15, no. 4, pp , [4] Ryu, J. F., Gweon, D.-G., and Moon, K. S., "Optimal design of a flexure hinge based XY0 wafer stage", Precision engineering, vol. 21 pp , [5] Speich, J. and Goldfarb, M., "A compliantmechanism-based three degree-of-freedom manipulator for small-scale manipulation", Robotica, vol. 18, no. 1, pp , [6] Smith, S.T.: Flexures: Elements of Elastic Mechanisms, Gordon & Breach, [7] Paros, J.M., Weisbord, L., 1965, How to Design Flexure Hinges, Machine Design, 25: [8] Hornbogen, E.: On the Term "Pseudo-elasticity, Z. Metallkunde, vol. 86-5, pp , [9] Hesselbach, J. and Raatz, A.: Pseudo-Elastic Flexure-Hinges in Robots for Micro Assembly, Proc. of SPIE, vol. 4194, pp , [10] Hesselbach, J., Raatz, A., Heuer, K., and Wrege, J.: Compliant Parallel Robots with Pseudo-Elastic Flexure Hinges, Proc. of the Intern. Precision Assembly Seminar, Austria, March, Ratchev, Delchambre (Edts.), pp , [11] Hesselbach, J., Becker, O., Dittrich, S, and Schlaich, P. "A New Hybrid 4-D.O.F.-Robot for Micro- 6

COMPLIANT PARALLEL ROBOTS Development and Performance

COMPLIANT PARALLEL ROBOTS Development and Performance Annika Raatz, Jan Wrege, Arne Burisch and Jiirgen Hesselbach Institute of Machine Tools and Production Technology (IWF), Technical Universiy Braunschweig,