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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 techno-logies have to be developed. As an alternative to conven-tional 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 micro-positioning 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

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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 stress-strain 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 re-transformation 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).

3mmR=15mm

0,15mmaxis of rotation x-axis

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 instanta-neous 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].

3 STRUCTURE OF THE PARALLEL ROBOT (TRIGLIDES)

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.

TCP

p

M

qi

x

y

z

primary axis

secondary axis

α

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)

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(a) spatial view (b) top view

(c) spatial view (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) 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 parallelo-grams and the working platform in the initial position of the structure with no deflections of the hinges.

(a) spatial view (b) top view

(c) (d)

Figure 5: Optimised workspace of the compliant robot (Triglides)

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.

deflection x [mm] min, max

y [mm] min, max

z [mm] min, max

workspace

± 180° -218,176 -206,206 -324,0 1

± 30° -202,176 -174,174 -314,-26 0.88

± 20° -138,138 -118,118 -282,-84 0.45

Table 1: Workspace dimensions of the structure 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 z-coordinates.

∆q∆y∆x

∆q∆rt

22 +== (1)

It can also be well seen that the shape of the workspace in a plane depends on the position of this plane in z-direction. 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.

1.6 1.3

1.02 0.820.92

(a) z = 100 mm (b) z = 200 mm

(d)(c)

x

z y

4

0.97 0.740.85

0.8 0.70.75

(c) z = 250 mm (d) z = 300 mm

Figure 6: Transmission ratio of the structure in different planes

4 COMPLIANT MECHANISM

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 primary axis, 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 7: Rotational axes of the flexure hinges and axes of the spatial parallelogram of the structure

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.

platform

secondary axes

primary axis

Figure 8: Design of the combined flexure hinge (2 DOF) with outer primary axis (o-pa design)

Figure 9: Design of the combined flexure hinge (2 DOF) with inner primary axis (i-pa design)

Designmodel

Mode number

Frequency

[Hz] Deformation mode

outer primary axis

1,2 92.9 pa-bending / torsion

3,4,5 114.7 torsion 6,7,8 115.2 torsion 9 126.5 pa-bending 10,11 140.4 pa-bending, sa-bending 12 141.7 sa-bending 13,14,15 150.8 sa-bending

secondary axis 1

secondary axis 2

primary axis

(a) (a) (b) (b)

(a) (a) (b) (b)

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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, torsion

24 218 pa-bending, sa-bending 25 235.4 pa-bending, sa-bending,

torsion 26 – 30 265.3 sa-bending inner-primary axis

1,2 10.4 pa-bending, sa- torsion

3 28.1 pa-torsion, sa- bending 4,5,6 67.6 pa-torsion, sa- bending 7,8 102.3 sa-bending, sa- torsion 9 117.9 pa-bending 10 118.2 sa-bending 11,12,13 131.8 sa-bending 14,15 151,6 sa-bending 16-21 167.6 –

174.8 sa- torsion

22 183.5 sa- torsion 23,24 194.5 sa- torsion, sa-bending 25,26,27 217.0 sa-bending 28,29,30 223 – 225 combination

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 primary axis 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 torsional moments should be better absorbed and trans-formed into tension and compression forces.

primary axis

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.

Figure 11: Compliant macro parallel robot (Triglides)

Figure 12: Working platform (view from bottom)

secondary axis 1

secondary axis 2

primary axis

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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. 6 REFERENCES [1] Merlet, J.P.: “Les robots parallèles”, Édition Hermes,

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