Flexure Mechanisms

Long-range Elastic Guidance Mechanisms for Electrostatic Comb-drive Actuators

The range of motion and output force of the often used electrostatic comb-drive with folded flexure straight guidance, as shown in Figure 1, is limited by sideways instability due to poor sideways stiffness of the folded flexure at relatively large deflections. For example at displacements larger than 20 times the leaf-springs thickness (t), the stiffness in x-direction has decreased by several orders of magnitude, causing sideways snap-in leading to limited travel and poor output force. The individual leaf-springs of the folded flexures would have to be 20μm thick and 5mm long for an output force of at least 100μN over a range of ±100μm. The stress due to deformation is generally not a limiting factor. We have designed, modeled, fabricated and tested several Watt’s and ‘Exact constrained folded flexures’. The combined device area of comb-drive and suspension has been minimized given a range of motion of 200μm, and an output force (electrostatic force minus elastic deformation force of the guidance) of at least 100μN over the full range of motion using a voltage limitation of 80V. The best performing mechanism, the ‘Exact constraint folded flexure’, shows that, compared to the folded flexure, the total device area has been reduced by a factor of 2.8 and the output force has been increased by a factor of 1.4 as shown in Table 1.

Pre-curved folded flexure guidance: http://www.youtube.com/watch?v=68Sdn25Gwwc
Exact constrained folded flexure guidance: http://www.youtube.com/watch?v=wOT41vktViI
Watt’s mechanism based guidance: http://www.youtube.com/watch?v=WHxiEjVSkWM
Roberts’ mechanism based guidance: http://www.youtube.com/watch?v=e21aV8tLvWY

Figure 1. The Folded flexure on the left, and the exact constraint folded flexure using a 1:2 lever and using an extra leaf-spring on the right.

Table 1. Comparison of several modeled elastic guidance mechanisms

Folded flexure

Exact constraint folded flexure

Double Watt’s

Range of motion

100 μm



Min. output force over range

100 μN



Area of 2 mechanisms

4.5 mm2

1.2 mm2

7.2 mm2

Area of actuator

0.85 mm2

0.63 mm2

0.67 mm2

Performance: Fmax . xmax / Atotal

3.2 mN·m/m2

12 mN·m/m2

7.0 mN·m/m2

Figure 2. Axial stiffness reduction at deflection of several modeled design variations of the ‘Exact constraint folded flexure’ and a standard folded flexure as a reference, where the shuttle is constraint in the y-direction.

Figure 3. (a) Performance of the ‘Exact constraint folded flexure’ for varying thickness (t) and length (l) of the flexures. The leaf-springs are prismatic and no extra flexure is incorporated. (b) Microscope pictures of the undeflected and (c) 100μm deflected ‘Exact constraint folded flexure’.

For more information:

D.M. Brouwer, A. Otten, J.B.C. Engelen, B. Krijnen and H.M.J.R. Soemers, Long-range Elastic Guidance Mechanisms for Electrostatic Comb-drive Actuators, Proc. of the EUSPEN Int. conf., Delft, the Netherlands, submitted.