Instantaneous Kinematics Analysis via Screw-Theory of a Novel 3-CRC Parallel Mechanism

This paper presents the mobility and kinematics analysis of a novel parallel mechanism that is composed by one base, one platform and three identical limbs with CRC joints. The paper obtains closed-form solutions to the direct and inverse kinematics problems, and determines the mobility of the mechanism and instantaneous kinematics by applying screw theory. The obtained results show that this parallel robot is part of the family 2R1T, since the platform shows 3 DOF, i.e.: one translation perpendicular to the base and two rotations about skew axes. In order to calculate the direct instantaneous kinematics, this paper introduces the vector mh, which is part of the joint velocity vector that multiplies the overall inverse Jacobian matrix. This paper compares the results between simulations and numerical examples using Mathematica and SolidWorks in order to prove the accuracy of the analytical results.

[1]  Daniel E. Whitney,et al.  The path method for analyzing mobility and constraint of mechanisms and assemblies , 2005, IEEE Transactions on Automation Science and Engineering.

[2]  Joseph K. Davidson,et al.  Robots and Screw Theory: Applications of Kinematics and Statics to Robotics , 2004 .

[3]  J. P. Merlet,et al.  Appropriate Design of Parallel Manipulators , 2008 .

[4]  Clément Gosselin,et al.  SHaDe, a new 3-DOF haptic device , 2002, IEEE Trans. Robotics Autom..

[5]  Jian S. Dai,et al.  A Study of the Mobility of a Family of 3-DOF Parallel Manipulators via Screw Theory , 2009 .

[6]  R. Clavel,et al.  A Fast Robot with Parallel Geometry , 1988 .

[7]  D. Stewart,et al.  A Platform with Six Degrees of Freedom , 1965 .

[8]  Lung-Wen Tsai,et al.  Jacobian Analysis of Limited-DOF Parallel Manipulators , 2002 .

[9]  Ernesto Rodriguez-Leal,et al.  Kinematic analysis of the 3-CUP parallel mechanism , 2013 .

[10]  Maria Zack.  The Geometry of Christopher Wren and Robert Hooke: A Walking Tour in London , 2011 .

[11]  R. Bricard.  Memoir on the Theory of the Articulated Octahedron , 2012, 1203.1286.

[12]  Jian S. Dai,et al.  Mobility Analysis and Inverse Kinematics of a Novel 2R1T Parallel Manipulator , 2011 .

[13]  Clément M. Gosselin,et al.  An initiative for the kinematics study of parallel manipula tors , 2013 .

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

[15]  Clément Gosselin,et al.  Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator , 2000 .

[16]  Jian S. Dai,et al.  Inverse Kinematics and Motion Simulation of a 2-DOF Parallel Manipulator with 3-PUP Legs , 2009 .

[17]  Jian S. Dai,et al.  Evolutionary Design of Parallel Mechanisms: Kinematics of a Family of Parallel Mechanisms with CentralizedMotion , 2010 .

[18]  V. Parenti-Castelli,et al.  Position Analysis in Analytical Form of the 3-PSP Mechanism , 2001 .

[19]  Qinchuan Li,et al.  1T2R Parallel Mechanisms Without Parasitic Motion , 2010, IEEE Transactions on Robotics.