A novel approach of input tolerance design for parallel mechanisms using the level set method

Input uncertainties inevitably result in the output error for parallel mechanisms, which will lead to significant influence on good work performance. To control the output error within the specification boundary, this article proposes a novel approach of input tolerance design based on the level set method for the driving joint. The implementation of the proposed method can be divided into two subtasks. First, using the level set method, the exact input error boundary is determined by means of evolving an initial input error interface with a defined normal speed field, thereby transforming the problem of exploring the exact boundary into solving a partial differential equation with initial value. On this basis, according to the equal and scaled principles, the tolerance width of each input is evaluated in an intuitionally geometrical manner, that is, searching the maximum geometry corresponding to the principle inside the exact input error boundary. Finally, two planar parallel mechanisms with different degrees of freedom are introduced as numerical examples to demonstrate the execution and effectiveness of the proposed method.

[1]  Serge Samper,et al.  Tolerance Analysis and Synthesis by Means of Deviation Domains, Axi-Symmetric Cases , 2007 .

[2]  Zuomin Dong,et al.  New Production Cost-Tolerance Models for Tolerance Synthesis , 1994 .

[3]  Wilma Polini,et al.  Assembly design in aeronautic field: From assembly jigs to tolerance analysis , 2017 .

[4]  Hans Nørgaard Hansen,et al.  Tolerance analysis in manufacturing using process capability ratio with measurement uncertainty , 2017 .

[5]  Spencer P. Magleby,et al.  Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments , 1998 .

[6]  D. Ravindran,et al.  Concurrent tolerance allocation and scheduling for complex assemblies , 2015 .

[7]  Stéphane Caro,et al.  A three-step methodology for dimensional tolerance synthesis of parallel manipulators , 2016 .

[8]  P K Singh,et al.  Important issues in tolerance design of mechanical assemblies. Part 1: Tolerance analysis , 2009 .

[9]  Jhy-Cherng Tsai,et al.  Optimal statistical tolerance allocation for reciprocal exponential cost–tolerance function , 2013 .

[10]  Jayaprakash Govindarajalu,et al.  Tolerance design of mechanical assembly using NSGA II and finite element analysis , 2012 .

[11]  Antonio Armillotta,et al.  Force analysis as a support to computer-aided tolerancing of planar linkages , 2015 .

[12]  Sébastien Briot,et al.  Accuracy analysis of 3-DOF planar parallel robots , 2008 .

[13]  K. Sankaranarayanasamy,et al.  Optimal tolerance design of assembly for minimum quality loss and manufacturing cost using metaheuristic algorithms , 2009 .

[14]  Xiaoyu Ding,et al.  Tolerance analysis of annular surfaces considering form errors and local surface deformations , 2018 .

[15]  Serge Samper,et al.  Tolerance Analysis and Synthesis by Means , 2007 .

[16]  A. Clément,et al.  A dimensioning and tolerancing assistance model for CAD/CAM systems , 1994 .

[17]  M. Shunmugam,et al.  A unified framework for tolerance analysis of planar and spatial mechanisms using screw theory , 2013 .

[18]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[19]  J. Sethian,et al.  LEVEL SET METHODS FOR FLUID INTERFACES , 2003 .

[20]  Alluru Gopala Krishna,et al.  Simultaneous optimal selection of design and manufacturing tolerances with different stack-up conditions using scatter search , 2006 .

[21]  P. Jain,et al.  Important issues in tolerance design of mechanical assemblies. Part 2: Tolerance synthesis , 2009 .

[22]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

[23]  S. Osher,et al.  A PDE-Based Fast Local Level Set Method 1 , 1998 .

[24]  Wilma Polini,et al.  Geometric Tolerance Analysis , 2011 .

[25]  Lazhar Homri,et al.  Tolerance analysis - Form defects modeling and simulation by modal decomposition and optimization , 2017, Comput. Aided Des..

[26]  Computing the worst case accuracy of a PKM over a workspace or a trajectory , 2008 .

[27]  Y. Ni,et al.  Error modeling and tolerance design of a parallel manipulator with full-circle rotation , 2016 .

[28]  Zouhaier Affi,et al.  Prediction of the pose errors produced by joints clearance for a 3-UPU parallel robot , 2009 .

[29]  Han S. Kim,et al.  The kinematic error bound analysis of the Stewart platform , 2000, J. Field Robotics.

[30]  Kenneth W. Chase,et al.  Design Issues in Mechanical Tolerance Analysis , 1998 .

[31]  Yanlong Cao,et al.  A novel tolerance analysis method for three-dimensional assembly , 2019 .

[32]  Genliang Chen,et al.  Output error bound prediction of parallel manipulators based on the level set method , 2010 .

[33]  Hao Wang,et al.  Tolerance analysis of mechanical assemblies based on the product of exponentials formula , 2018 .

[34]  N. Jawahar,et al.  Optimal Pareto front for manufacturing tolerance allocation model , 2017 .

[35]  Kuei-Yuan Chan,et al.  Kinematic error analysis and tolerance allocation of cycloidal gear reducers , 2018, Mechanism and Machine Theory.

[36]  D Vignesh Kumar,et al.  Tolerance allocation of complex assembly with nominal dimension selection using Artificial Bee Colony algorithm , 2019 .

[37]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[38]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[39]  Martin Leary,et al.  Application of Polynomial Chaos Expansion to Tolerance Analysis and Synthesis in Compliant Assemblies Subject to Loading , 2015 .

[40]  Chao Liu,et al.  Analytical method for optimal component tolerances based on manufacturing cost and quality loss , 2013 .

[41]  Joseph K. Davidson,et al.  Using tolerance maps to validate machining tolerances for transfer of cylindrical datum in manufacturing process , 2014 .

[42]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .