Synthesis of precision serial flexure systems using freedom and constraint topologies (FACT)

Abstract In this paper we introduce the principles necessary to synthesize the complete body of serial flexure system concepts, which satisfy desired design requirements using Freedom and Constraint Topologies (FACT). FACT utilizes a comprehensive library of geometric shapes that represent regions were constraints may be placed for synthesizing flexure systems that possess designer-specified degrees of freedom (DOFs). Prior to the theory of this paper, FACT was limited to the synthesis of parallel flexure systems only. The ability to synthesize serial flexure systems is important because serial flexure systems (i) may possess DOFs not accessible to parallel flexure systems, (ii) exhibit larger ranges of motion, and (iii) enable cancellation of parasitic errors. Geometric shapes that represent motions only accessible to serial flexure systems have been derived and added to the existing body of FACT shapes initially intended for parallel flexure synthesis only. Systematic rules and guidelines have been created that help designers use these shapes to generate every parallel and serial flexure concept that satisfies the desired functional requirements. We demonstrate how to use these shapes to utilize or avoid underconstraint in serial flexure synthesis. A serial flexure system is designed that interfaces the lead screw of a lathe to the carriage that it drives as a case study to demonstrate the theory of this paper.

[1]  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 .

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

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

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

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

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

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

[8]  Jian S. Dai,et al.  Interrelationship between screw systems and corresponding reciprocal systems and applications , 2001 .

[9]  Judy M. Vance,et al.  A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms , 2009 .

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

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

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

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

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

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

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

[17]  Layton Carter Hale,et al.  Principles and Techniques for Designing Precision Machines , 2013 .

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

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

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

[21]  Zhen Huang,et al.  Study on the kinematic characteristics of 3 DOF in-parallel actuated platform mechanisms , 1996 .

[22]  Larry L. Howell,et al.  A compliant end-effector for microscribing , 2005 .

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

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

[25]  Jonathan B. Hopkins,et al.  Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part I—General Methodology , 2010 .

[26]  Jian S. Dai,et al.  Mobility analysis of a complex structured ball based on mechanism decomposition and equivalent screw system analysis , 2004 .

[27]  Larry L. Howell,et al.  Compliant high-precision E-quintet ratcheting (CHEQR) mechanism for safety and arming devices , 2007 .

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

[29]  Hai-Jun Su,et al.  ON LINE SCREW SYSTEMS AND THEIR APPLICATION TO FLEXURE SYNTHESIS , 2010 .

[30]  Zhen Huang,et al.  Kinematic characteristics analysis of 3 DOF in-parallel actuated pyramid mechanism☆ , 1996 .

[31]  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..

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

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

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

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

[36]  Jonathan B. Hopkins,et al.  Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part III—Numerations and Synthesis of Flexure Mechanisms , 2010 .