Design of Flexure-based Precision Transmission Mechanisms using Screw Theory

This paper enables the synthesis of flexure-based transmission mechanisms that possess multiple decoupled inputs and outputs of any type (e.g. rotations, translations, and/or screw motions), which are linked by designer-specified transmission ratios. A comprehensive library of geometric shapes is utilized from which every feasible concept that possesses the desired transmission characteristics may be rapidly conceptualized and compared before an optimal concept is selected. These geometric shapes represent the rigorous mathematics of screw theory and uniquely link a body's desired motions to the flexible constraints that enable those motions. This paper's impact is most significant to the design of nano-positioners, microscopy stages, optical mounts, and sensors. A flexure-based microscopy stage was designed, fabricated, and tested to demonstrate the utility of the theory.

[1]  I-Ming Chen,et al.  Micromanipulation System Design Based on Selective Actuation Mechanisms , 2006, Int. J. Robotics Res..

[2]  Jonathan B. Hopkins,et al.  A screw theory basis for quantitative and graphical design tools that define layout of actuators to minimize parasitic errors in parallel flexure systems , 2010 .

[3]  Jonathan B. Hopkins,et al.  Corrigendum to Synthesis of multi-degree of freedom, parallel flexure system concepts via Freedom and Constraint Topology (FACT)—Part I: Principles , 2010 .

[4]  Charles Kim,et al.  A Building Block Approach to the Conceptual Synthesis of Compliant Mechanisms Utilizing Compliance and Stiffness Ellipsoids , 2008 .

[5]  Jonathan B. Hopkins,et al.  Synthesis of multi-degree of freedom, parallel flexure system concepts via freedom and constraint topology (FACT). Part II: Practice , 2010 .

[6]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[7]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[8]  Jack Phillips,et al.  Freedom in Machinery: Volume 1, Introducing Screw Theory , 1985 .

[9]  Jonathan B. Hopkins,et al.  Synthesis of precision serial flexure systems using freedom and constraint topologies (FACT) , 2011 .

[10]  Charles Kim.  Functional Characterization of Compliant Building Blocks Utilizing Eigentwists and Eigenwrenches , 2008 .

[11]  Jonathan B. Hopkins,et al.  Design of parallel flexure systems via Freedom and Constraint Topologies (FACT) , 2007 .

[12]  A. Midha,et al.  Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms , 1995 .

[13]  Joseph Duffy,et al.  Classification of screw systems—I. One- and two-systems , 1992 .

[14]  Jean-Pierre Merlet.  Singular Configurations of Parallel Manipulators and Grassmann Geometry , 1989, Int. J. Robotics Res..

[15]  Xianwen Kong,et al.  Type Synthesis of Parallel Mechanisms , 2010, Springer Tracts in Advanced Robotics.

[16]  Shusheng Bi,et al.  A Method to Evaluate and Calculate the Mobility of a General Compliant Parallel Manipulator , 2004 .

[17]  H. Lipkin,et al.  Mobility of Overconstrained Parallel Mechanisms , 2006 .

[18]  J. Michael McCarthy,et al.  Conditions for line‐based singularities in spatial platform manipulators , 1998 .

[19]  Mary Frecker,et al.  Topological synthesis of compliant mechanisms using multi-criteria optimization , 1997 .

[20]  Jonathan B. Hopkins,et al.  Design of flexure-based motion stages for mechatronic systems via Freedom, Actuation and Constraint Topologies (FACT) , 2010 .

[21]  J. M. Selig,et al.  On the compliance of coiled springs , 2004 .

[22]  McCarthy,et al.  Geometric Design of Linkages , 2000 .

[23]  Z. Huang,et al.  Type Synthesis of Symmetrical Lower-Mobility Parallel Mechanisms Using the Constraint-Synthesis Method , 2003, Int. J. Robotics Res..

[24]  Charles J. Kim,et al.  An Instant Center Approach Toward the Conceptual Design of Compliant Mechanisms , 2006 .

[25]  Sridhar Kota,et al.  Strategies for systematic synthesis of compliant mems , 1994 .

[26]  K. Waldron.  The constraint analysis of mechanisms , 1966 .

[27]  C. Barus.  A treatise on the theory of screws , 1998 .

[28]  Yuefa Fang,et al.  Structure Synthesis of a Class of 4-DoF and 5-DoF Parallel Manipulators with Identical Limb Structures , 2002, Int. J. Robotics Res..

[29]  Joseph Duffy,et al.  Classification of screw systems—II. Three-systems , 1992 .

[30]  Sridhar Kota,et al.  Topological Synthesis of Compliant Mechanisms Using Linear Beam Elements* , 2000 .

[31]  Joseph Duffy,et al.  Orthogonal spaces and screw systems , 1992 .

[32]  K. H. Hunt,et al.  Geometry of screw systems1Screws: Genesis and geometry , 1990 .

[33]  K. H. Hunt,et al.  Geometry of screw systems—2: classification of screw systems , 1990 .