This paper introduces a three degree of freedom XYZ Micromanipulator (XYZM) that is fabricated in the $x$-$y$ plane and positions components in the $x$, $y$, and $z$ directions using three independent linear inputs. The mechanism positions components on a platform using three legs, each composed of a slider mechanism and a parallelogram mechanism.Three versions of the XYZM were fabricated and tested using surface micromachining processes: the rigid-body, offset, and compliant XYZM. Slider displacements of 45 micrometers result in a predicted out-of-plane displacement of 188 micrometers for the rigid-body XYZM, 205 micrometers for the offset XYZM, and 262 micrometers for the compliant XYZM.

This paper introduces the force analysis of the XYZ Micromanipulator (XYZM). The XYZM has three independent linear inputs and a positioning platform. The positioning platform remains horizontal throughout its motion and has translation in the x, y, and z directions. The design and displacement analysis for the XYZM was reported previously. This paper concentrates on the input-output force relationships and the derivation of the XYZM kinematic coefficients. Equations for the three versions of the XYZM are reported and sample results provided. Slider displacements of 45 micrometers result in a predicted out-of-plane displacement of 188 micrometers for the rigid-body XYZM and 262 micrometers for the compliant XYZM. This correlates to output force of 286 micronewtons with an input force of 150 micronewtons for the rigid-body XYZM and 261 micronewton output force with an input force of 150 micronewtons for the compliant XYZM.

This paper introduces the XZ Micropositioning Mechanism (XZMM) that is fabricated in the x-y plane and translates components in the x-z direction using one linear input. The positioning platform of the mechanism remains parallel to the substrate throughout its motion. The XZMM has been tested and actuated using thermal actuation and achieves an out-of-plane output displacement of 41 micrometers with a 27 micrometer x-direction input.

Clamshell casting is a popular manufacturing technique where liquid is poured into a mold or cast and the cast is removed once the liquid has hardened. The term clamshell refers to the way in which the cast is removed. The two cast parts are removed by rotation through a hinge much like a clamshell. Given an object, modeled by a polyhedron P of arbitrary genus with combinatorial complexity n , we determine when the surface of the polyhedron can be decomposed into two parts s.t. each part can be rotated around a line in space without colliding with each other or intersecting the interior. Such a line is a valid casting line. Specifically, we solve the following problems: (1) Given a line l in space, we determine in ( )O n time whether l is a valid casting line for P . If degeneracies are present, such as a reflex edge or face of P is perpendicular to l , the running time increases slightly to ( log ) O n n . (2) In 4 ( ( )) α O n n time, where ( ) α n is the inverse Ackermann function, we report all combinatorially distinct valid casting lines. The running time is 4 ( log ) O n n in the presence of degeneracies. All of the running times are shown to be almost optimal.

No abstract