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A method for designing and optimnizing compliant mechanisms is provided, in addition to bistable compliant mechanism designs. According to the method, a selected compliant structure may be modeled analytically, and the characteristics of the analytical model may be optimized. Multiple recursive opt

A method for designing and optimnizing compliant mechanisms is provided, in addition to bistable compliant mechanism designs. According to the method, a selected compliant structure may be modeled analytically, and the characteristics of the analytical model may be optimized. Multiple recursive optimization algorithms may be used, for example, to determine the general location of a global optimum, and then to determine the values of the analytical model characteristics that obtain the global optimum or a feasible configuration for the selected compliant structure. Geometric characteristics of the selected compliant structure may be derived from the values of the analytical model characteristics. Bistable compliant designs may have a shuttle disposed between a pair of base members. The shuttle (20) may be linked to the base members (22, 24) by a pair of legs (30, 32), via flexural pivots. The base members may have cantilevered mounting beams to create deformable mounts that receive and store potential energy. The stable configurations are those in which the stored potential energy is at a relative minimum.

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What is claimed is: 1. A method for determining a desired value of at least one geometric characteristic for a selected compliant structure configured to have at least one objective characteristic, the method comprising: creating an analytical model of the selected compliant structure, the analytic

What is claimed is: 1. A method for determining a desired value of at least one geometric characteristic for a selected compliant structure configured to have at least one objective characteristic, the method comprising: creating an analytical model of the selected compliant structure, the analytical model having a plurality of substantially rigid elements connected by at least one joint, the analytical model having at least one analytical model characteristic corresponding to the geometric characteristic; applying a first recursive optimization algorithm to determine a first value of the analytical model characteristic; and deriving the desired value of the geometric characteristic from the analytical model characteristic. 2. The method of claim 1, wherein the selected compliant structure comprises a plurality of geometric characteristics, each of which has a corresponding analytical model characteristic. 3. The method of claim 1, further comprising determining at least one mathematical relationship between the analytical model characteristic and the objective characteristic. 4. The method of claim 3, wherein the first recursive optimization algorithm iteratively uses the mathematical relationship to determine a value of the objective characteristic for each of a plurality of values of the analytical model characteristic. 5. The method of claim 1, wherein the desired value of the geometric characteristic is derived from the first value of the analytical model characteristic. 6. The method of claim 1, wherein the first recursive optimization algorithm comprises simulated annealing. 7. The method of claim 1, further comprising applying a second recursive optimization algorithm to the first value to determine a second value of the analytical model characteristic. 8. The method of claim 7, wherein the desired value of the geometric characteristic is derived from the second value of the analytical model characteristic. 9. The method of claim 8, wherein the second recursive optimization algorithm comprises generalized reduced gradient. 10. The method of claim 9, wherein the first value is proximate a global optimum of the objective characteristic. 11. The method of claim 10, wherein the second value is within a threshold range of the global optimum of the objective characteristic. 12. The method of claim 1, wherein the analytical model further comprises at least one of the group consisting of linear springs and torsional springs. 13. The method of claim 1, wherein the selected compliant structure includes at least one semi-rigid link connected by at least one small-length flexural pivot. 14. The method of claim 13, wherein the geometric characteristics of the semi-rigid link and the small-length flexural pivot are selected from the group consisting of the width of the small-length flexural pivot, the out-of-plane thickness of the semi-rigid link, the out-of-plane thickness of the small-length flexural pivot, the modulus of elasticity of the compliant structure material, the length of the semi-rigid link, the length of the small-length flexural pivot, and the initial angle between the small-length flexural pivot and the semi-rigid link. 15. The method of claim 1, wherein the selected compliant structure comprises a compliant bistable mechanism. 16. The method of claim 1, wherein the selected compliant structure comprises a compliant micromechanism. 17. A method for determining desired values of a plurality of geometric characteristics for a selected compliant structure configured to have at least one objective characteristic, the method comprising: establishing initial geometric characteristics of the selected compliant structure, wherein the initial geometric characteristics define an interim configuration; applying a first recursive optimization algorithm wherein a random geometric characteristic of the interim configuration is changed and the randomly changed geometric characteristic is integrated into and redefines the interim configuration according to an objective comparison algorithm, wherein the first recursive optimization algorithm iterates until the interim configuration is proximate a global optimum; applying a second recursive optimization algorithm wherein a vector is created by adjusting geometric characteristics of the interim configuration such that the vector identifies a number of improved geometric characteristics, wherein the improved geometric characteristics are integrated into the interim configuration, the second recursive optimization algorithm iterating until the interim configuration is within a threshold range of the global optimum; and establishing the desired values of the geometric characteristics for the selected compliant structure from the geometric characteristics of the globally optimized interim configuration. 18. The method of claim 17, wherein the objective comparison algorithm comprises: comparing the interim configuration, incorporating the randomly changed geometric configuration, to the objective characteristic; and performing one of the following: selecting a configuration that approaches the operational characteristic; rejecting a configuration that does not approach the operational characteristic; or selecting a configuration that does not approach the operational characteristic through the use of a stochastic method. 19. The method of claims 18, wherein the annealing algorithm is based upon a cooling schedule of a metal annealing process. 20. The method of claim 17, wherein the selected compliant structure is a bistable compliant mechanism. 21. The method of claim 20, wherein the first recursive optimization algorithm identifies at least one bistable state of the bistable compliant mechanism. 22. The method of claim 17, wherein the selected compliant structure is a compliant micromechanism. 23. The method of claim 17, wherein the initial geometric characteristics of the interim configuration are derived from a finite element analysis of the selected compliant structure. 24. The method of claim 17, wherein the first recursive optimization algorithm comprises a simulated annealing method. 25. The method of claim 17, wherein the second recursive optimization algorithm comprises a generalized reduced gradient method. 26. The method of claim 17, wherein at least one geometric characteristic of the selected compliant structure is held constant during the first recursive optimization algorithm. 27. The method of claim 17, wherein at least one geometric characteristic of the selected compliant structure is held constant during the second recursive optimization algorithm. 28. A method for determining desired values of a plurality of analytical characteristics for a selected compliant structure configured to have at least one objective characteristic, the method comprising: establishing initial analytical characteristics of the selected compliant structure, wherein the initial analytical characteristics define an interim configuration; applying a first recursive optimization algorithm wherein a random analytical characteristic of the interim configuration is changed and the randomly changed analytical characteristic is integrated into and redefines the interim configuration according to an objective comparison algorithm, wherein the first recursive optimization algorithm iterates until the interim configuration is proximate a global optimum; applying a second recursive optimization algorithm wherein a vector is created by adjusting analytical characteristics of the interim configuration such that the vector identifies a number of improved analytical characteristics, wherein the improved analytical characteristics are integrated into and redefine the interim configuration, the second recursive optimization algorithm iterating until the interim configuration is within a threshold range of the global optimum; and establishing the desired values of the analytical characteristics for the selected compliant structure from the analytical characteristics of the globally optimized interim configuration. 29. A method for determining desired values of a plurality of analytical characteristics for a selected compliant structure configured to have at least one objective characteristic, the method comprising: determining a desired objective characteristic to be obtained for the selected compliant structure; creating an analytical model of the selected compliant structure, the analytical model having a plurality of substantially rigid elements connected by at least one joint, the analytical model having a plurality of analytical model characteristics corresponding to the analytical model, wherein the analytical model characteristics define an interim configuration; applying a first recursive optimization algorithm wherein a random analytical model characteristic of the interim configuration is changed and the randomly changed analytical model characteristic is integrated into and redefines the interim configuration according to an objective comparison algorithm, wherein the first recursive optimization algorithm iterates until the interim configuration is proximate a global optimum; applying a second recursive optimization algorithm wherein a vector is created by adjusting the analytical model characteristics of the interim configuration such that the vector identifies a number of improved analytical model characteristics, wherein the improved analytical model characteristics are integrated into and redefine the interim configuration, the second recursive optimization algorithm iterating until the interim configuration is within a threshold range of the global optimum; determining the desired values of the analytical characteristics that correspond to the values of the analytical model characteristics. 30. A micromechanism having a first stable configuration and a second stable configuration, the micromechanism comprising: a first base member; a first beam section coupled to the first base member; a solid and rigid shuttle integrally formed with the base member such that the shuttle is translatable between a first low potential energy position corresponding to the first stable configuration and a second low potential energy position corresponding to the second stable configuration, wherein the shuttle is sized for use in microelectromechanical systems; and a flexural pivot connecting the shuttle to the first beam section, wherein the flexural pivot has a thinner cross-section than the first beam section. 31. The micromechanism of claim 30 further comprising: a second base member; and a second beam section coupled to the second base member, wherein the first and second beam sections are disposed on either side of the shuttle such that the first beam section, the rigid shuttle, and the second beam section form a compliant bridge, the shuttle forming a central portion of the compliant bridge. 32. The micromechanism of claim 31 wherein the shuttle extends substantially perpendicular to the first and second beam sections to receive an input force. 33. The micromechanism of claim 30 wherein the mass of the shuttle is selected to move the micromechanism between the first and second stable configurations at a predetermined acceleration. 34. The micromechanism of claim 30 wherein the shuttle is positioned to close an electrical circuit in only one of the first position and the second position. 35. The micromechanism of claim 30 wherein the shuttle is positioned to selectively abut an actuator to receive an input force from the actuator. 36. The micromechanism of claim 30 wherein the shuttle is attached to an actuator to receive an input force from the actuator. 37. The micromechanism of claim 30 wherein the micromechanism is positioned to be toggled between low potential energy positions by a thermal microactuator. 38. The micromechanism of claim 30 wherein the micromechanism is positioned to be toggled between low potential energy positions by an electrostatic actuator. 39. A micromechanism having a first stable configuration and a second stable configuration, the micromechanism comprising: a solid and rigid shuttle sized for use in microelectromechanical systems, wherein the shuttle is translatable between a first low potential energy position corresponding to the first stable configuration and a second low potential energy position corresponding to the second stable configuration; a first leg coupled to the shuttle; and a first deformable mount coupled to the first leg such that the shuttle, the first leg, and the first deformable mount are integrally formed, the first deformable mount having a plurality of deformed configurations in which the shuttle is disposed between the first and second positions such that the first deformable mount urges the shuttle toward one of the first position and the second position, the first deformable mount further having an undeformed configuration. 40. The micromechanism of claim 39 wherein the first deformable mount comprises a mounting beam fixed between two anchors. 41. The micromechanism of claim 39 wherein the first deformable mount comprises a mounting beam cantilevered from a single anchor. 42. The micromechanism of claim 39 wherein the first deformable mount comprises a mounting beam with an arch shape in the undeformed configuration. 43. The micromechanism of claim 39 wherein the first deformable mount is disposed in one of the deformed configurations in at least one of the first stable configuration and the second stable configuration. 44. The micromechanism of claim 39 wherein the first deformable mount comprises a member directly coupled to the first leg, wherein the member is configured to provide resilient force in proportion to deflection of the member. 45. The micromechanism of claim 39 wherein the first leg is arched. 46. The micromechanism of claim 39 further comprising: a second leg coupled to the shuttle; and a second deformable mount coupled to the second leg, wherein the second leg and second deformable mount are integrally formed with the shuttle. 47. The micromechanism of claim 46 further comprising: a third leg coupled to the first deformable mount and the shuttle; and a fourth leg coupled to the second deformable mount and the shuttle; a second leg coupled to the second deformable mount, wherein the first and second legs are disposed on either side of the shuttle such that the first leg, the second leg, and the shuttle form a compliant bridge, the shuttle forming a central portion of the compliant bridge. 48. The micromechanism of claim 39 further comprising a third leg coupled to the shuttle and the first deformable mount. 49. The micromechanism of claim 39 further comprising a third leg coupled to a second deformable mount, wherein the first and second deformable mounts are aligned in series and bound at the ends by anchors. 50. The micromechanism of claim 39 wherein the first leg comprises a plurality of sections coupled to move relative to each other. 51. A micromechanism having a first stable configuration and a second stable configuration, the micromechanism comprising: a solid and rigid shuttle with a first low potential energy position corresponding to the first stable configuration and a second low potential energy position corresponding to the second stable configuration; a first leg; a first shuttle pivot coupling disposed between the shuttle and the leg; a first base member; and a first base pivot coupling disposed between the leg and the base member; wherein the shuttle, the first leg, the first shuttle pivot coupling, the first base member, and the first base pivot coupling are all integrally formed with each other, and wherein at least one of the first shuttle pivot coupling and the first base pivot coupling has a longitudinal length different from a longitudinal length of the first leg. 52. The micromechanism of claim 51 wherein the shuttle pivot coupling comprises a small-length flexural pivot integrally formed with the shuttle and the first leg. 53. The micromechanism of claim 51 wherein the shuttle pivot coupling comprises a pin joint. 54. The micromechanism of claim 51 wherein the base pivot coupling comprises a small-length flexural pivot integrally formed with the first base member and the first leg. 55. The micromechanism of claim 51 wherein the base pivot coupling comprises a pin joint. 56. The micromechanism of claim 51 further comprising: a second leg; a second shuttle pivot coupling disposed between the shuttle and the second leg; a second base member; and a second base pivot coupling disposed between the second leg and the second base member. 57. The micromechanism of claim 51 wherein the base member is a deformable mount. 58. A micromechanism having a first stable configuration and a second stable configuration, the micromechanism comprising: a first base member; a second base member separated from the first base member by an offset distance; and a compliant bridge coupled to and integrally formed with the first and second base members, wherein the compliant bridge has a nonuniform longitudinal length and is disposable along a first path corresponding to the first stable configuration and a second path corresponding to the second stable configuration, wherein each of the first and second paths is longer than the offset distance, wherein the compliant bridge comprises a solid and rigid shuttle. 59. The micromechanism of claim 58 wherein the compliant bridge comprises an arched beam with a first end pivotally coupled to the first base member and a second end pivotally coupled to the second base member. 60. The micromechanism of claim 58 further comprising: a first mounting beam cantilevered to the first base member to form a first deformable mount; and a second mounting beam cantilevered to the second base member to form a second deformable mount. 61. The micromechanism of claim 58 wherein the compliant bridge comprises a beam having a first beam section coupled to the first base member, a second beam section coupled to the second base member, and wherein the shuttle is disposed between the first and second beam sections to from a central portion of the beam. 62. The micromechanism of claim 58 wherein the shuttle extends substantially perpendicular to the first path. 63. The micromechanism of claim 58 wherein the compliant bridge comprises: a first leg coupled to the first base member; a second leg coupled to the second base member; and the shuttle is coupled between the first and second legs. 64. The micromechanism of claim 58 wherein the micromechanism toggles between stable configurations when an electrical current passes through and elongates the compliant bridge. 65. A micromechanism having a first stable configuration and a second stable configuration, wherein the micromechanism is a bistable accelerometer, the micromechanism comprising: an electrical connection; a first base member; a shuttle integrally formed with the base member such that the shuttle is translatable between a first low potential energy position corresponding to the first stable configuration and a second low potential energy position corresponding to the second stable configuration, wherein the shuttle contacts the electrical connection in the second stable configuration to close a circuit, wherein the mass of the shuttle is selected to move the micromechanism between the first and second stable configurations at a predetermined acceleration. 66. The micromechanism of claim 65 further comprising a first beam section coupled to the first base member and a flexural pivot connecting the shuttle to the first beam section, wherein the flexural pivot has a thinner cross-section than the first beam section. 67. The micromechanism of claim 65 further comprising: a second base member; a first beam section coupled to the first base member; and a second beam section coupled to the second base member, wherein the first and second beam sections are disposed on either side of the shuttle such that the first beam section, the shuttle, and the second beam section form a compliant bridge, the shuttle forming a central portion of the compliant bridge.