Micromechanics and Microactuators pp 4960  Cite as
Flexure HingeBased Parallel Manipulators Enabling HighPrecision Micro Manipulations
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Abstract
Parallel manipulators are very suitable for the realization of planar and spatial highprecision micro manipulations, especially with flexure hinges bringing many advantages. The goal is to investigate the possibility of flexure hinges being implemented into parallel manipulators. The characteristics of typical flexure hinges are compared at first. Orthogonal parallel manipulators with a regular spatial translation of the moving platform are assessed afterwards. For a dimensioned flexure hinge and a selected parallel manipulator, a flexure hingebased parallel manipulator is monolithically designed and analysed.
Keywords
Flexure hinges Parallel manipulators Flexure hingebased parallel manipulators1 Introduction
A serial manipulator has one kinematic chain with a fixed base and a moving platform at the ends. Between them, links are serially connected by actuated joints and therefore heavily loaded. For this reason, a low positioning accuracy and a poor load capacity are available. A significant stiffness enhancement without strengthening individual links can be attained by using parallel kinematic structures. In a parallel manipulator, a moving platform is coupled with a fixed base by several separate kinematic chains, socalled limbs. Because of load distribution on the limbs, a good load capacity and a high positioning accuracy are achieved. The dynamic behaviour is also improved [1]. Parallel manipulators are very suitable for the realization of planar and spatial highprecision micro manipulations. Highprecision requirements are met best with parallel kinematic structures, whose limited working spaces are not drawbacks for micro manipulations. A micro manipulation typically covers a working space up to millimetre range and a positioning accuracy up to nanometre range. Such a small working space and such a high positioning accuracy do not demand an extreme miniaturization, so that a micro manipulator is distinguished from a micro machine [2]. However, the micro manipulator can be implemented hardly with conventional joints, but successfully with flexure hinges. They make a monolithic design possible, which is characterized primarily by a radical reduction of backlash and friction [3]. Some applications of flexure hingebased parallel manipulators should be mentioned: sample positioning in microscopy, wafer lithography, manufacture and assembly in precision engineering and micro system technology, etc.
2 Requirements
The selection of degrees of freedom of the moving platform depends on the function of a micro manipulator. All six degrees of freedom ensure a full mobility, but that entails high costs and a complex control. Three or four degrees of freedom are usually sufficient for a micro manipulation, namely three translations, if necessary enhanced with one rotation. The remaining degrees of freedom have to be kinematically constrained.
In precision engineering, the working space of the moving platform is normally a couple of cubic millimetres large. Since the installation space for a micro manipulator is often quite restricted, a relatively wide motion range of the flexure hinges is necessary. The motion accuracy of the flexure hinges has to be as high as possible at the same time.
Because of a monolithic design (practically no backlash in flexure hinges), environmental disturbances mainly affect the repeatability of the moving platform. Therefore, the mechanical stability (a high stiffness) and the thermal stability (a low thermal expansion) of a micro manipulator are of vital importance. Concerning calibration costs, the positioning accuracy of the moving platform should also not be neglected.
Physical properties of Ti6Al4 V used in further research
Physical property  Symbol  Value 

Mass density  ρ  4430 kg/m^{3} 
Modulus of elasticity  E  114 GPa 
Shear modulus  G  44 GPa 
Yield strength  σ_{0,2}  885 MPa 
Endurance strength  σ_{D}  515 MPa 
In this paper, the characteristics (motion range and accuracy, stiffness) of typical (corner filleted notch and right circular notch) flexure hinges are compared at first. A few orthogonal parallel manipulators (3 PRRRR, 3 PRRR and 3 ΠRΠR) with a regular spatial translation of the moving platform are assessed afterwards. For a dimensioned (right circular notch) flexure hinge and a selected parallel manipulator (3 ΠRΠR), a flexure hingebased parallel manipulator is monolithically designed by means of pseudorigidbody modelling and analysed by means of finiteelement method. Accordingly, the parasitic rotations of the moving platform, the maximum stress in the flexure hinges and the stiffness of the micro manipulator are determined.
3 Flexure Hinges
Design parameters of flexure hinges used in further research (see Fig. 3)
Corner filleted notch (r = 0.2 mm)  l = 2 mm  t = 0.4 mm  b = 20 mm 

Right circular notch  R = 2 mm  t = 0.4 mm  b = 20 mm 
Maximum stress and rotation axis drift of flexure hinges for rotation angle of ±0.02 rad (FEM)
Flexure hinge  Max. stress  Axis drift 

Corner filleted notch  263.1 MPa  5.067 μm 
Right circular notch  419.2 MPa  3.699 μm 
Stiffness  In contrast to a conventional joint, theoretically with no stiffness in moving directions and an infinitely high stiffness in constrained directions, a flexure hinge possesses a finite stiffness in all directions. Accordingly, it is necessary to achieve adequate stiffness ratios between moving and constrained directions by the design of flexure hinges.
Stiffness values of flexure hinges
Load type  Corner filleted notch  Right circular notch 

Bending around rotation axis  6.08 Nm/rad  11.54 Nm/rad 
Bending around constrained axis  15.20 kNm/rad  17.06 kNm/rad 
Eigenfrequencies of flexure hinges (FEM)
Eigenmodes  Corner filleted notch  Right circular notch 

Bending around rotation axis  10.27 Hz  13.93 Hz 
Bending around constrained axis  372.5 Hz  381.8 Hz 
Torsion around constrained axis  367.1 Hz  538.8 Hz 
Because of more suitable characteristics (motion accuracy, torsion stiffness), the right circular flexure hinge is implemented into a selected parallel manipulator here.
4 Parallel Manipulators
Various approaches have been used for the structure synthesis of parallel manipulators with fewer than six degrees of freedom. They have usually been based either on the group theory [9] or on the screw theory [10]. A combined approach including the group theory and the screw theory with the specifics of micro manipulation is applied here. The results are also compared with those of other approaches [11].
Three limb structures being able to build orthogonal parallel manipulators with a regular spatial translation of the moving platform are preselected and briefly assessed below.

+ The maximum rotation angles of all the joints are similar.

− The installation size is large because of an inline arrangement of the links and the linear actuator.

− The maximum rotation angle of the intermediate revolute joint is approximately two times larger than those of the peripheral revolute joints in case of the same link lengths in the limb.

+ Because of an angular arrangement of the links and the linear actuator, the installation size is small.

+ The maximum rotation angles of all the joints are similar.

+ Because of an angular arrangement of the links, the installation size is small.
5 Monolithic Design
Rotation angles of conventional revolute joints for given displacements of moving platform and optimized rigid link lengths in case of orthogonal parallel manipulator with ΠRΠR limbs (PRBM)
Rotation angles of joints [rad]  

Displacements of moving platform [mm]  Joint 1  Joints 2, 3, 4, 5  Joint 6  Joints 7, 8, 9, 10  
Limb X  Limb Y  Limb Z  Limb X  Limb Y  Limb Z  Limb X  Limb Y  Limb Z  Limb X  Limb Y  Limb Z  
2  0  0  0.0002  0.0000  0.0184  0.0000  0.0202  0.0000  0.0002  0.0000  0.0184  0.0168  0.0002  0.0032 
2  2  0  0.0186  0.0002  0.0184  0.0000  0.0202  0.0202  0.0186  0.0002  0.0184  0.0202  0.0170  0.0034 
2  2  2  0.0186  0.0186  0.0186  0.0202  0.0202  0.0202  0.0186  0.0186  0.0186  0.0202  0.0202  0.0202 
6 Results
Maximum stress in flexure hinges (FEM)
 Case 1  Case 2  Case 3 

Critical hinges  2,3,4,5  2,3,4,5  2,3,4,5 
σ_{max} [MPa]  413.6  418.8  426.9 
Eigenmodes and eigenfrequencies of micro manipulator (FEM)
 Translation  Rotation 

Non active drives  ≥ 19.7 Hz  ≥ 496.9 Hz 
Active drives    ≥ 553.9 Hz 
Displacements and corresponding parasitic rotations of moving platform (FEM)
 Case 1  Case 2  Case 3 

x [mm]  2.0  2.0  2.0 
y [mm]  0.0  2.0  2.0 
z [mm]  0.0  0.0  2.0 
θx [μrad]  1.4  341.7  212.4 
θy [μrad]  129.3  130.7  212.4 
θz [μrad]  343.0  213.8  212.4 
7 Summary
Two typical (corner filleted notch and right circular notch) flexure hinges are dimensioned according to the motion range and compared at first. The right circular notch flexure hinge shows more suitable characteristics (motion accuracy, torsion stiffness) for the implementation into a parallel manipulator. Using a systematic approach, three limb structures (PRRRR, PRRR and ΠRΠR) being able to build orthogonal parallel manipulators with a regular spatial translation of the moving platform are preselected and briefly assessed. Favourable characteristics of the ΠRΠR limb are highlighted. For the dimensioned right circular notch flexure hinge and the selected orthogonal parallel manipulator with three ΠRΠR limbs, a micro manipulator is monolithically designed and analysed. Thereby, small parasitic rotations of the moving platform and a high stiffness of the micro manipulators are achieved. Therefore, a further research through the realization and the test of an experimental model is intended.
References
 1.Merlet, J.P., Parallel robots, Springer, 2006.Google Scholar
 2.Pernette, E., Henein, S., Magnani, I., Clavel, R., Design of parallel robots in microrobotics, Robotica, Vol. 15, 1997, 417420.CrossRefGoogle Scholar
 3.Smith, S., T., Flexures, Elements of elastic mechanisms, Gordon and Breach, 2000.Google Scholar
 4.Trease, B., P., Moon, Y.M., Kota, S., Design of largedisplacement compliant joints, Journal of mechanical design, Vol. 127, 2005, 788798.CrossRefGoogle Scholar
 5.Lobontiu, N., Compliant mechanisms, Design of flexure hinges, CRC Press, 2003.Google Scholar
 6.Xu, Q., Li, Y., Mechanical design of compliant parallel micromanipulators for nano scale manipulation, International conference on nano/micro engineered and molecular systems, 2006, 653657.Google Scholar
 7.Koseki, Y., Tanikawa, T., Koyachi, N., Arai, T., Kinematic analysis of translational 3DoF micro parallel mechanism using matrix method, International conference on intelligent robots and systems, 2000, 786792.Google Scholar
 8.Koseki, Y., Arai, T., Sugimoto, K., Takatuji, T., Goto, M., Design and accuracy evaluation of highspeed and high precision parallel mechanism, International conference on robotics and automation, 1998, 13401345.Google Scholar
 9.Herve, J., M., The Lie group of rigid body displacements, a fundamental tool for mechanism design, Mechanism and machine theory, Vol. 34, 1999, 719730.MathSciNetzbMATHCrossRefGoogle Scholar
 10.Kong, X., Gosselin, C., M., Type synthesis of 3DoF translational parallel manipulators based on screw theory, Journal of mechanical design, Vol. 126, 2004, 8392.CrossRefGoogle Scholar
 11.Carricato, M., ParentiCastelli, V., A family of 3DoF translational parallel manipulators, Journal of mechanical design, Vol. 125, 2003, 302307.CrossRefGoogle Scholar
 12.Howell, L., L., Compliant mechanisms, Wiley, 2001Google Scholar