Stiffness Design for a Spatial Three Degrees of Freedom Serial Compliant Manipulator Based on Impact Configuration Decomposition

This paper proposes a method of stiffness design for a spatial Three Degrees of Freedom (3DOF) serial compliant manipulator with the objective of protecting the compliant joint actuators when the manipulator comes up against impact. System dynamic equations of serial compliant manipulators integrated with an impact model are linearized to identify the maximum joint torques in the impact. Based on this, a general procedure is given in which maximum joint torques are calculated with different directions of end-effector velocity and impact normal in the manipulator workspace based on a given magnitude of end-effector velocity. By tuning the stiffness for each compliant joint to ensure the maximum joint torque does not exceed the maximum value of the actuator, candidate stiffness values are obtained to make the compliant actuators safe in all cases. The theory and procedure are then applied to the spatial 3DOF serial compliant manipulator of which the impact configuration is decomposed into a 2DOF planar serial manipulator and a 1DOF manipulator with a 2DOF link based on the linearized impact-dynamic model. Candidate stiffness of the 3DOF serial compliant manipulator is obtained by combining analysis of the 2DOF and 1DOF manipulators. The method introduced in this paper can be used for both planar and spatial compliant serial manipulators.

[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]  Burak Demirel,et al.  Semicompliant Force Generator Mechanism Design for a Required Impact and Contact Forces , 2010 .

[3]  Alessandro De Luca,et al.  Collision Detection and Safe Reaction with the DLR-III Lightweight Manipulator Arm , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[4]  Thomas G. Sugar,et al.  A Robotic “Jack Spring”™ for Ankle Gait Assistance , 2005 .

[5]  Jian S. Dai,et al.  Stiffness characteristics and kinematics analysis of two-link elastic underactuated manipulators , 2002, J. Field Robotics.

[6]  Michael Yu Wang.  A Kinetoelastic Formulation of Compliant Mechanism Optimization , 2009 .

[7]  Alin Albu-Schäffer,et al.  Safety Evaluation of Physical Human-Robot Interaction via Crash-Testing , 2007, Robotics: Science and Systems.

[8]  Clément Gosselin,et al.  A Quasi-Static Model for Planar Compliant Parallel Mechanisms , 2009 .

[9]  Saeed Behzadipour,et al.  Variable Stiffness Spring Using Tensegrity Prisms , 2010 .

[10]  Antonio Bicchi,et al.  Design and Control of a Variable Stiffness Actuator for Safe and Fast Physical Human/Robot Interaction , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[11]  Sridhar Kota,et al.  An intrinsic geometric framework for the building block synthesis of single point compliant mechanisms , 2011 .

[12]  Guimin Chen,et al.  A Tristable Mechanism Configuration Employing Orthogonal Compliant Mechanisms , 2010 .

[13]  Hong Zhou,et al.  Topology Optimization of Compliant Mechanisms Using the Improved Quadrilateral Discretization Model , 2012 .

[14]  Ou Ma,et al.  Model order reduction for impact-contact dynamics simulations of flexible manipulators , 2007, Robotica.

[15]  Hai-Jun Su.  Mobility Analysis of Flexure Mechanisms via Screw Algebra , 2011 .

[16]  Wenjing Wang,et al.  New Approach to the Dynamic Modeling of Compliant Mechanisms , 2010 .

[17]  H. Su,et al.  Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy , 2007 .

[18]  Sadao Kawamura,et al.  Resonance-based motion control method for multi-joint robot through combining stiffness adaptation and iterative learning control , 2009, 2009 IEEE International Conference on Robotics and Automation.

[19]  Jian S. Dai,et al.  Compliance Analysis of a Three-Legged Rigidly-Connected Platform Device , 2006 .

[20]  Oussama Khatib,et al.  A hybrid actuation approach for human-friendly robot design , 2008, 2008 IEEE International Conference on Robotics and Automation.

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

[22]  Oussama Khatib,et al.  Design and development of high-performance torque-controlled joints , 1995, IEEE Trans. Robotics Autom..

[23]  Sébastien Briot,et al.  On the Dynamic Properties of Rigid-Link Flexible-Joint Parallel Manipulators in the Presence of Type 2 Singularities , 2010 .

[24]  David E. Orin,et al.  Design of Series-Elastic Actuators for Dynamic Robots With Articulated Legs , 2009 .

[25]  Shusheng Bi,et al.  A Novel Family of Leaf-Type Compliant Joints: Combination of Two Isosceles-Trapezoidal Flexural Pivots , 2009 .

[26]  Veljko Potkonjak,et al.  Dynamics of contact tasks in robotics. Part I: general model of robot interacting with environment , 1999 .

[27]  Jian S. Dai,et al.  Dynamics and Coupling Actuation of Elastic Underactuated Manipulators , 2003, J. Field Robotics.

[28]  Nikolaos G. Tsagarakis,et al.  A compact soft actuator unit for small scale human friendly robots , 2009, 2009 IEEE International Conference on Robotics and Automation.

[29]  G. Hirzinger,et al.  A new variable stiffness design: Matching requirements of the next robot generation , 2008, 2008 IEEE International Conference on Robotics and Automation.

[30]  Matthew M. Williamson,et al.  Series elastic actuators , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[31]  Jian S. Dai,et al.  Stiffness Modeling of the Soft-Finger Contact in Robotic Grasping , 2004 .

[32]  N. G. Tsagarakis,et al.  Analysis and Development of a Semiactive Damper for Compliant Actuation Systems , 2013, IEEE/ASME Transactions on Mechatronics.

[33]  John Kenneth Salisbury,et al.  A New Actuation Approach for Human Friendly Robot Design , 2004, Int. J. Robotics Res..

[34]  Jian S. Dai,et al.  Characteristic Equation-Based Dynamics Analysis of Vibratory Bowl Feeders With Three Spatial Compliant Legs , 2008, IEEE Transactions on Automation Science and Engineering.

[35]  Beno Benhabib,et al.  Stiffness optimization for two-armed robotic sculpting , 2008, Ind. Robot.

[36]  Jerry E. Pratt,et al.  Intuitive control of a planar bipedal walking robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[37]  G. K. Ananthasuresh,et al.  A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms , 2009 .

[38]  Inna Sharf,et al.  Literature survey of contact dynamics modelling , 2002 .

[39]  Bishakh Bhattacharya,et al.  Forward and Inverse Analyses of an SMA Actuated Compliant Link , 2011 .

[40]  Charles Kim.  Design Strategies for the Topology Synthesis of Dual Input-Single Output Compliant Mechanisms , 2009 .

[41]  Gordon Cheng,et al.  Full-Body Compliant Human–Humanoid Interaction: Balancing in the Presence of Unknown External Forces , 2007, IEEE Transactions on Robotics.

[42]  T. Takenaka,et al.  The development of Honda humanoid robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[43]  Just L. Herder,et al.  Negative Stiffness Building Blocks for Statically Balanced Compliant Mechanisms: Design and Testing , 2010 .

[44]  Yousheng Yang,et al.  HyQ - Hydraulically actuated quadruped robot: Hopping leg prototype , 2008, 2008 2nd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics.

[45]  Oussama Khatib,et al.  Analysis of torque capacities in hybrid actuation for human-friendly robot design , 2010, 2010 IEEE International Conference on Robotics and Automation.