Chapter 5. Static Non-Linear Analysis of Parallel Kinematic
XY Flexure Mechanisms
In this chapter we present the static non-linear analysis for some of the XY flexure mechanism designs
that were proposed in Chapter 2. Based on the derivations and approximations presented in Chapters 3
and 4, the analysis here is carried out with the objective of evaluating the attributes and resulting
performance measures of these XY flexure mechanism designs. The attributes that are of concern were
explained in Chapter 2, and are repeated here briefly.
1) Specific range of motion: One of the fundamental limitations of flexure mechanisms in general is
their small range of motion, whereas improved specific range is desirable in many applications.
2) Parasitic yaw error of the motion stage: For the sake of large range of motion, and to minimize the
number of actuated axes, it is desirable to passively achieve small yaw of the motion stage.
3) Cross-axis coupling: A force or displacement input along one axis should result in minimal
displacement of the motion stage along the other axis, so as to reduce the dependence on end-point
feedback and calibration.
4) Actuator Isolation: The point of force application on the mechanism should not be affected by forces
and displacements in other directions, so as to reduce the dependence on a decoupler, which limits the
range of motion and the axial stiffness between the stage and the actuator.
5) In-line Axial Stiffness: Change in the axial stiffness of constituent flexure units that lie between the
actuator and the motion stage, as a consequence of displacements and applied forces, is important in