Lamina emergent mechanisms (LEMs) are mechanical devices fabricated from a planar material (a lamina) and have motion that emerges out of the fabrication plane (Figure 1). They achieve their motion from the deflection of flexible members (and are therefore compliant mechanisms [1]) and are monolithic. The beauty of LEMs lies in their potential to perform sophisticated mechanical tasks with simple topology. The ability to fabricate them from planar layers of material makes it possible to manufacture LEMs using simplified processes from sheet materials. High-performance, compact devices can be fabricated at low manufacturing cost, but with the tradeoff of challenging design.

                                                                           Figure 1

Characteristics and Advantages

Advantages inherent in the nature of LEMs are: being fabricated in a plane, having a flat initial state, being monolithic, and allowing interaction for multiple LEMs. Each of these characteristics and its associated advantages are briefly described below.

Planar fabrication

The fact that LEMs can be fabricated from planar layers influences both what processes can be used for their manufacture and what materials may be used in their construction. At the micro level, LEMS can be fabricated using single-layer MEMS fabrication methods and materials, which offers significant cost and reliability advantages. It also provides opportunities for complex out-of-plane motion with only a single layer.

At the macro level, manufacturing processes used to make static structures or components for assembly can be used to create mechanisms capable of sophisticated motions and complex tasks. Example processes include stamping, fine blanking, laser cutting, water jet cutting, plasma cutting, and wire electrical discharge machining (EDM). Some of these processes, such as stamping, offer significant cost advantages for high-volume production.

Planar fabrication also allows the use of sheet goods to directly create mechanisms. The use of low-cost, high-quality sheet goods has the potential to dramatically reduce cost for high-volume production. It also makes possible the next characteristic: flat initial state.

Flat initial state

The fabricated state of LEMs provides opportunities for extreme compactness. Compact mechanisms are particularly attractive in applications with highly constrained space. Another advantage is found in applications where it is important for the device to be compact during transport and then deployed when at its location of operation. An obvious advantage of a flat initial state is compact packaging and shipping, which can mean a significant reduction in the cost of handling, storing, and  shipping high volumes of devices. For MEMS, a flat state in the as-fabricated position is a requirement for common fabrication methods.

Monolithic

The single-piece nature of LEMs brings with it many of the characteristics of compliant mechanisms in general. The creation of controlled motion without pin joints provides opportunities for increased precision because of the elimination of backlash and wear. Weight can be reduced by using compliant mechanisms, and friction between rubbing parts can be reduced or eliminated. Assembly of mechanism parts is unnecessary.

Interaction between LEMs

More sophisticated devices are made possible by creating mechanisms of multiple layers, with each layer having the benefits of LEMs. Layers may be fused to create a monolithic device, or multiple LEMs may interact. An example of such a multi-layer LEM (MLEM) is seen in Figure 2 below.

                                                                               Figure 2

Challenges Inherent in LEMs Design and Research

The advantages for lamina emergent mechanisms are compelling reasons to pursue their development. However, the advantages do not come without challenges, the most important of which are described below.

Nonlinear

The desired motions are too large to be modeled using linearized equations such as those commonly used in beam equations or linear finite element analysis. Thus, any successful modeling approach must be capable of addressing the intrinsic nonlinearities of the problem.

Singularities

There are singularities inherent in LEM analysis because of the planar nature of the fabricated position. LEMs are change-point mechanisms in their fabricated state, and multiple motions are possible for a given input. A related problem exists for metamorphic mechanisms, and separate models will likely be required for devices in their pre- and post-morphed states.

Coupled

Unlike those in rigid-body mechanisms, the motions in LEMs are highly coupled with stress, fatigue, and energy stored in a system. This results in more complicated analysis with more variables and constraints.

Design

Although the analysis is difficult, the real challenge at hand is not the analysis of existing LEMs, but the design of lamina emergent mechanisms that have not previously been possible. The creation of advanced LEMs will require the integration of the best available theories and compliant mechanism development experience.

Adaptive Morphing Systems (Metamorphic Mechanisms)

A metamorphic mechanism is a “mechanism whose number of effective links changes as it moves from one configuration to another” [2]. Metamorphic transformations of LEMs may allow them to start in their natural change-point state but, through one or more transformations, be changed to form different mechanisms (or structures) that do not have change-point characteristics [3-4]. Several important types of metamorphic mechanisms recently presented in the literature are described below. 

Foldable/erectable mechanisms

An example of a foldable/erectable metamorphic mechanism is a cardboard box made by folding and connecting the folds of a piece of cardboard stock [2, 5-6]. As the piece is folded and the different segments contact each other, the degrees of freedom are reduced until, in the end, the piece of stock that once had multiple degrees of freedom becomes a rigid structure. 

Deployable structures

Although not always recognized as such, many deployable structures are metamorphic mechanisms. Pre-assembly entities are erected into the final structure through post tensioning or by other means. Several different deployable truss configurations that have been developed [7-11], and spatial mechanisms have recently been proposed as elements of deployable structures [12-17]. 

Kinematotrophic mechanisms

Kinematotrophic mechanisms [18-19] are kinematic chains whose connectivity and mobility change as a result of continuous variations in position variables. 

Contact-aided compliant mechanisms

At some point during the movement of contact-aided compliant mechanisms [20-21], one of the links of the mechanism touches another link and acts like a cam, providing additional resistance [22-23]. After touching the contact, the behavior of the mechanism.

Current Research

Actuation of LEMs

Most of the research in LEMs to date has focused on their motion and force-deflection aspects. A key to the continued advancement of LEMs and their applications is the development of actuation approaches to allow them to move. This research is currently underway, and will provide an essential groundwork for the development and commercialization of many useful LEMs.

LEM actuation is challenging because most traditional methods of actuation are not consistent with the advantages of LEMs. One advantage is low cost, a characteristic that an actuator would ideally meet. Another advantage is the planar nature, which is essential for an internal actuator. LEM actuators must meet the following criteria:

1. The actuator must have enough displacement and force capability to be feasible for use in macro-scale LEMs.
2. The actuator’s dimensions must be consistent with the planar nature of LEMs.
3. The actuator must be able to be incorporated into the design of a LEM.

Recent research in actuation has shown the conceptual feasibility of shape memory alloys (SMAs) as direct actuators, as well as piezoelectrics as triggers. Additionally, concepts involving electromagnets and other adaptations of traditional actuators are being researched. In some applications, a LEM could be set into motion by a bulkier traditional actuator situated externally, with extensions to reach the LEM inside an assembly. This is similar to the concept of extended pruners, actuated by the pull of a rope, to cut high branches.

Spherical LEMs and LEM Joints 

Research was recently completed in this area which resulted in the development of a classification for spherical 4R LEMs that extended into spherical 6R LEMs and arrays of spherical mechanisms. Currently work is being done on the development of a new LEM joint. The most commonly used LEM joint is the LET (Lamina Emergent Torsion) joint which allows for large rotations but does not possess adequate off-axis stiffness. The joint in development is designed to be stiffer in the off-axis directions (especially in tension and compression) while remaining rotationally flexible.

References

[1]  Howell, L. L. (2001). Compliant Mechanisms. New York: John Wiley & Sons.

[2] Dai, J. S., and Jones, J. R. (1999). “Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds.” Journal of Mechanical Design, Vol. 121, No. 3, pp. 375–382.

[3] Dai, J. S. and Jones, J. R. (2005) “Matrix representation of topological changes in metamorphic mechanisms.” Journal of Mechanical Design, Vol. 127, No. 4, pp. 837-840.

[4] Kuo, C. H. and Yan, H. S. (2007) “On the Mobility and Configuration Singularity of Mechanisms With Variable Topologies.” Journal of Mechanical Design, Vol. 129, No. 6, pp. 617-624.

[5] Liu, H., and Dai, J. S. (2002). “Carton Manipulation Analysis Using Configuration Transformation.” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 216, No. 5, pp. 543–555.

[6] Dai, J. S., and Qixian, Z. (2000). “Metamorphic Mechanisms and their Configuration Models.” Chinese Journal of Mechanical Engineering, Vol. 13, No. 3, pp. 212–218.

[7] Dehdashti, G., and Schmidt, L. C. (1995). “Barrel-Vault Space Trusses Shaped by Posttensioning.” Journal of Structural Engineering, Vol. 121, No. 12, pp. 1758–1764.

[8] Schmidt, L. C., and Li, H. (1995). “Geometric Models of Deployable Metal Domes.” Journal of Architectural Engineering, Vol. 1, No. 3, pp. 115–120.

[9] Dehdashti, G., and Schmidt, L. C. (1996). “Dome-Shaped Space Trusses Formed by Means of Posttensioning.” Journal of Structural Engineering, Vol. 122, No. 10, pp. 1240–1245.

[10] Onoda, J., Fu, D. Y., and Minesugi, K. (1995). “Two-Dimensional Deployable Hexapod Truss.” Journal of Spacecraft and Rockets, Vol. 33, No. 3, pp. 416–421.

[11] Takamatsu, K. A., and Onoda, J. (1991). “New Deployable Truss Concepts for Large Antenna Structures or Solar Concentrators.” Journal of Spacecraft and Rockets, Vol. 28, No. 3, pp. 330–338.

[12] Gan, W, and Pellegrino, S (2006). “Numerical Approach to the Kinematic Analysis of Deployable Structures Forming a Closed Loop.” Proceedings of the I MECH E Part C Journal of Mechanical Engineering Science, Vol. 220, No. 7, pp. 1045-1056.

[13] Chen, Y. and You, Z. (2005). “Mobile Assemblies Based on the Bennett Linkage.” Proceedings of the Royal Society A, Vol. 461, pp. 1229–1245.

[14] Chen, Y. and You, Z. (2004). “Deployable Structures Based on the Bricard Linkages.” Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Palm Springs, California, April 19-22. AIAA 2004-1604.

[15] Baker, J. E. (2007). “Kinematic Investigation of the Deployable Bennett Loop.” ASME Journal of Mechanical Design, Vol. 129, No. 6, pp. 602-610.

[16] Baker, J. E. (2006). “On Generating a Class of Foldable Six-Bar Spatial Linkages.” ASME Journal of Mechanical Design, Vol. 128, No. 2, pp. 374-383.

[17] Melin, Nicholas O'Brien (2004), “Application of Bennett Mechanisms to Long-Span Shelters.” Ph.D Dissertation, University of Oxford, Oxford, England.

[18] Wolhart K. (1996). Kinematotropic Mechanisms, Recent Advances in Robot Kinematics, Kluwer, pp. 359–368.

[19] Galletti, C., and Giannotti, E. (2002). “Multiloop Kinematotrophic Mechanisms.” Proceedings of the 2002 ASME Design Engineering Technical Conferences, pp. 455-460.

[20] Mankame, N. D., and Ananthasuresh, G. K. (2002). “Contact Aided Compliant Mechanisms: Concept and Preliminaries.” Proceedings of the ASME Design Engineering Technical Conferences, DETC2002/MECH-34211.

[21] Mankame, N. D., and Ananthasuresh, G. K. (2004). “Topology Synthesis of Path-Generating Contact-aided Compliant Mechanisms Using a Regularized Contact Model.” Paper presented at 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York.

[22] Mackay, A. B., Magleby, S. P. and Howell, L. L. (2007). “A Pseudo-Rigid-Body Model for Rolling-Contact Compliant Beams.” Proceedings of the 2007 ASME Design Engineering Technical Conferences, DETC2007-35536.

[23] Mankame, N.D. and Ananthasuresht, G.K. (2006). “Synthesis of contact-aided compliant mechanisms for non-smooth path generation.” Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Vol. 4, pp. 2281-2303.