 
Summary: Title: Parasitic Errorfree Symmetric Diaphragm Flexure, and a set of precision
compliant mechanisms based it: Three and Five DOF flexible torque couplings,
Five DOF motion stage, single DOF linear/axial bearing.
Inventors: Shorya Awtar, Alexander H. Slocum
Three Degrees of Freedom (DOF) Diaphragm Flexures
Diaphragm flexures are commonly used for providing motion in the direction normal to
the flexure plane. Many versions of the design shown in Fig.1 have been frequently
encountered in the literature and in numerous devices/applications [13]. Because of its
geometry, apart from a Z translation, this flexure is also compliant in roll and pitch
motions (i.e. rotations about the X and Y axes). Any diaphragm flexure made from thin
sheetmetal will typically have these three degrees of freedom, and will be very stiff in the
two planer directions, X and Y, and in yaw (i.e. rotation about the Z axis). An evident
drawback of this design is that it suffers from a parasitic Ztwist associated with Z
translation. The reason is for this twist becomes obvious when one recognizes that each
of the peripheral arms (or blades) in this design behaves like a fixedfree cantilever, as
shown in Fig.2. For a fixedfree cantilever, any motion in the desired direction is
associated with a transverse motion e, also referred to as parasitic error motion, so as to
maintain a constant arc length of the cantilever. Theory of linear elasticity provides us
with the following results
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