Geometric Constraint and Mobility Variation of Two 3SvPSv Metamorphic Parallel Mechanisms

This paper presents a unique feature of geometric constraint of adjacent axes of the variable-axis (vA) joint and analyses the effectiveness in the constructed limb, resulting in variation of mobility configuration of two 3SvPSv metamorphic parallel mechanisms. The underlying principle of the metamorphosis of this vA joint is unravelled by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the vA joint from the source phase Sv to the variable Hooke’s joint phase Uv and the variable revolute-joint phase Rv. The kinematic chain installed with the vA joint forms a reconfigurable limb and is then used to construct two 3SvPSv metamorphic parallel mechanisms proposed in this paper. The phase change of the vA joints incurs the constraint change of the SvPSv limb and subsequently results in the change of mobility configuration of the metamorphic parallel mechanisms. The paper further addresses the geometrical condition for constructing 3SvPSv metamorphic parallel mechanisms following the constraints delivered by the reconfigurable limbs, leading to the analysis of mobility change of the mechanisms induced by the phase change of the limbs.

[1]  Jian S. Dai,et al.  Mobility Change in Two Types of Metamorphic Parallel Mechanisms , 2009 .

[2]  Jian S. Dai,et al.  Biological Modeling and Evolution Based Synthesis of Metamorphic Mechanisms , 2008 .

[3]  Yuefa Fang,et al.  Enumeration of a class of overconstrained mechanisms using the theory of reciprocal screws , 2004 .

[4]  Jian S. Dai,et al.  From Origami to a New Class of Centralized 3-DOF Parallel Mechanisms , 2007 .

[5]  N. Orlandea,et al.  Parallel Structures and Their Applications in Reconfigurable Machining Systems , 2002 .

[6]  Jian S. Dai,et al.  Editorial preface in Reconfigurable Mechanisms and Robots , 2009 .

[7]  J. R. Jones,et al.  Matrix Representation of Topological Changes in Metamorphic Mechanisms , 2005 .

[8]  Jian S. Dai,et al.  Origami-based robotic paper-and-board packaging for food industry , 2010 .

[9]  L. W. Tsai,et al.  Robot Analysis: The Mechanics of Serial and Parallel Ma-nipulators , 1999 .

[10]  Y. G. Srinivasa,et al.  Characterization of reconfigurable Stewart platform for contour generation , 2009 .

[11]  Jian S. Dai,et al.  Topology and Constraint Analysis of Phase Change in the Metamorphic Chain and Its Evolved Mechanism , 2010 .

[12]  Jian S. Dai,et al.  Geometry and Constraint Analysis of the Three-Spherical Kinematic Chain Based Parallel Mechanism , 2010 .

[13]  G. Gogu.  Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations , 2004 .

[14]  Jian S. Dai,et al.  Reconfiguration of Spatial Metamorphic Mechanisms , 2009 .

[15]  Jian S. Dai,et al.  Inverse-kinematics-based control of a redundantly actuated platform for rehabilitation , 2009 .

[16]  C. Gosselin,et al.  Type Synthesis of Parallel Mechanisms With Multiple Operation Modes , 2007 .

[17]  Xilun Ding,et al.  Reconfiguration Theory of Mechanism From a Traditional Artifact , 2010 .

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

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

[20]  Q. Liao,et al.  Constraint analysis on mobility change of a novel metamorphic parallel mechanism , 2010 .

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

[22]  Kornel Ehmann,et al.  Design of a Novel 4-DOF Kinematotropic Hybrid Parallel Manipulator , 2011 .

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

[24]  Guanfeng Liu,et al.  Advantages and dynamics of parallel manipulators with redundant actuation , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[25]  Jian S. Dai,et al.  Finite Displacement Screw Operators With Embedded Chasles' Motion , 2012 .

[26]  Hong-Sen Yan,et al.  Topological Representations and Characteristics of Variable Kinematic Joints , 2006 .

[27]  J. Dai,et al.  Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds , 1998 .

[28]  D. Caldwell,et al.  Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism That Eliminates Singularities and Improves Dexterity , 2008 .

[29]  Grigore Gogu,et al.  Branching singularities in kinematotropic parallel mechanisms , 2009 .