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RESEARCH PAPERS

# Design Space of Single-Loop Planar Folded Micro Mechanisms With Out-of-Plane Motion

[+] Author and Article Information
Craig P. Lusk

Department of Mechanical Engineering, University of South Florida, 4202 East Fowler Avenue ENB 118, Tampa, FL 33620-5350clusk2@eng.usf.edu

Larry L. Howell1

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602lhowell@et.byu.edu

The design space $U4$ is topologically equivalent to the Real Projective Plane (12).

1

Corresponding author.

J. Mech. Des 128(5), 1092-1100 (Nov 03, 2005) (9 pages) doi:10.1115/1.2216734 History: Received May 06, 2005; Revised November 03, 2005

## Abstract

Microelectromechanical systems (MEMS) are usually fabricated using planar processing methods such as surface micromachining, bulk micromachining, or LIGA-type fabrication. If a micro mechanism is desired that has motion out of the plane of fabrication, it can be a folded mechanism in its fabricated position. The desire to design MEMS for a wide range of out-of-plane motions has led to the need for a better theoretical understanding of the design space for folded mechanisms. Thus, this paper derives the design space of arbitrary planar folded mechanisms. This results in the definition of the orientation set measures equality condition (OSMEC) which can be used in constructing adjacency set patches and joining them to construct the design space. The results can be used to explore different properties of the mechanisms in the design space. One such property, the mechanisms’ folded length, is given as an example. Although MEMS provide the primary motivation for the work, the results are general and apply to other areas of application.

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Topics: Design , Mechanisms

## Figures

Figure 1

A typical folded micromechanism in its folded configuration (4)

Figure 2

The folded micromechanism from Fig. 1 in an out-of-plane configuration (4)

Figure 3

A folded N-bar: (a) A sketch of an example N-bar mechanism, and (b) a vector loop representation of the same mechanism

Figure 4

Schematic depiction of joints: (a) open joint, (b) right-closed joint, and (c) left-closed joint

Figure 5

A vector representation of the folded mechanisms described in Table 1

Figure 6

The design space, U4, (a cuboctahedron) of four-bar folded mechanisms. Points on the same face represent mechanisms whose links are partitioned in the same way into orientation sets. Antipodal points on the cuboctahedron represent the front and back sides of the same mechanism.

Figure 7

A second representation of the design space of four-bar folded mechanisms with redundant (antipodal) points removed

Figure 8

A plot of y=abs(x), which shows the corner resulting from a change in the form of the absolute value function from when x<0, where y=abs(x)=−x, to the form y=abs(x)=x, when x>0

Figure 9

Figure 10

Four-bar adjacency set patches representing mobile mechanisms: (a) Patch C31: Linkages ρ1+ρ2=−(ρ3+ρ4), (b) Patch C24: Linkages satisfying ρ4+ρ1=−(ρ2+ρ3), (c) Patch D2413: Linkages satisfying ρ1+ρ3=−(ρ2+ρ4)

Figure 11

The combination of Euclidean simplexes to form adjacency set patches. (a) The combination of a 0-simplex with a 2-simplex. (b) The combination of two 1-simplexes.

Figure 12

Schematics of the three basic patches of a five-bar folded mechanism: (a) Tetrahedral shaped patch type B: ρ5=−(ρ1+ρ2+ρ3+ρ4), (b) wedge-shape patch type C: ρ4+ρ5=−(ρ1+ρ2+ρ3), (c) wedge-shaped patch type D: ρ3+ρ5=−(ρ1+ρ2+ρ4). The mechanisms represented by patch types B and C have a plication of two and the mechanisms represented by patch type D have a plication of four.

Figure 13

Nondimensionalized length of four-bar folded mechanisms with plication of Q=4

Figure 14

A vector representation of mechanisms corresponding to points β2413 and A as shown in Fig. 1 and described in Table 4

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