Modified chain algorithm to study planar compliant mechanisms

Interactive simulations in Virtual Reality, such as haptic interaction, are more and more used to test or optimize nonlinear mechanical systems subjected to large deformations. FE algorithms are often not suitable for such purposes due to the high computational burden and the long simulation times. This paper provides a modified version of the classic chain algorithm, referred to as modified chain algorithm (MCA), to overcome some convergency issues and reduce the simulation time. The proposed algorithm is able to reduce the number of iterations estimating two kind of average moment laws. The MCA is then integrated into a design optimization procedure for the synthesis of a double slider-crank compliant mechanism to be used as opening system for an adjustable bicycle saddle. Finally, a X-Y layered ABS prototype is manufactured by rapid prototyping technique and 3-D printer. Experimental setup to test the deflection of the prototype revealed in good accordance with results coming from the MCA.

[1]  Ashok Midha,et al.  Methodology for Compliant Mechanisms Design: Part II - Shooting Method and Application , 1992 .

[2]  Shorya Awtar,et al.  A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Strain Energy Formulation , 2010 .

[3]  Selçuk Güçeri,et al.  Mechanical characterization of parts fabricated using fused deposition modeling , 2003 .

[4]  Brian D. Jensen,et al.  Modeling of Large Deflection Members , 2013 .

[5]  B. Weiss,et al.  Clinical syndromes associated with bicycle seats. , 1994, Clinics in sports medicine.

[6]  Georges Dumont,et al.  Haptic manipulation of deformable CAD parts with a two-stage method , 2011 .

[7]  Charles H.-T. Wang,et al.  Shootingoptimization technique for large deflection analysis of structural members , 1992 .

[8]  Tommaso Ingrassia,et al.  VirDe: a new virtual reality design approach , 2009 .

[9]  Larry L. Howell,et al.  A Simplified Pseudo-Rigid-Body Model for Fixed-Fixed Flexible Segments , 2002 .

[10]  Roberto Raffaeli,et al.  An integrated methodology for the functional design of dental prosthesis , 2013 .

[11]  S. Scherer,et al.  Advanced visualization for finite elements analysis in virtual reality environments , 2008 .

[12]  A. Mamourian,et al.  Digital three‐dimensional modelling of the male pelvis and bicycle seats: impact of rider position and seat design on potential penile hypoxia and erectile dysfunction , 2007, BJU international.

[13]  Kok-Meng Lee,et al.  Computational models for predicting the deflected shape of a non-uniform, flexible finger , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[14]  H. B. Harrison Post-buckling analysis of non-uniform elastic columns , 1973 .

[15]  Shorya Awtar,et al.  A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation , 2010 .

[16]  I. Goldstein,et al.  Bicycle riding, perineal trauma, and erectile dysfunction: Data and solutions , 2007, Current urology reports.

[17]  Shijun Liao,et al.  An explicit solution of the large deformation of a cantilever beam under point load at the free tip , 2008 .

[18]  Andrew Nealen,et al.  Physically Based Deformable Models in Computer Graphics , 2006, Comput. Graph. Forum.

[19]  Brett A. Coulter,et al.  Numerical analysis of a generalized plane ‘elastica’ with non‐linear material behaviour , 1988 .

[20]  Ashok Midha,et al.  An Introduction to Mechanical Advantage in Compliant Mechanisms , 1998 .

[21]  Ashok Midha,et al.  A Graphical, User-Driven Newton-Raphson Technique for Use in the Analysis and Design of Compliant Mechanisms , 1990 .

[22]  T D Noakes,et al.  Effects of a novel bicycle saddle on symptoms and comfort in cyclists. , 2002, South African medical journal = Suid-Afrikaanse tydskrif vir geneeskunde.

[23]  Nicolae Lobontiu,et al.  Compliant Mechanisms: Design of Flexure Hinges , 2002 .

[24]  A. Palazotto,et al.  Large-deformation analysis of flexible beams , 1996 .

[25]  Alessandro Paoli,et al.  A CAE approach for the stress analysis of gear models by 3D digital photoelasticity , 2015 .

[26]  Kjell Mattiasson,et al.  Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals , 1981 .

[27]  G Breda,et al.  Development of a new geometric bicycle saddle for the maintenance of genital-perineal vascular perfusion. , 2005, The journal of sexual medicine.

[28]  R. Barbagallo,et al.  Interactive re-design of a novel variable geometry bicycle saddle to prevent neurological pathologies , 2016 .

[29]  Ashok Midha,et al.  Methodology for Compliant Mechanisms Design: Part I - Introduction and Large-deflection Analysis , 1992 .

[30]  J. L. Meek,et al.  Geometrically nonlinear analysis of space frames by an incremental iterative technique , 1984 .

[31]  Brian D Lowe,et al.  Nocturnal penile tumescence and rigidity testing in bicycling patrol officers. , 2002, Journal of andrology.

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

[33]  Pierre Villon,et al.  A model reduction approach for real-time part deformation with nonlinear mechanical behavior , 2007 .