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Research Papers

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

[+] Author and Article Information
Dongming Gan

Robotics Institute,
Khalifa University of Science, Technology and
Research,
127788, Abu Dhabi, UAE;
Advanced Robotics Department,
Istituto Italiano di Tecnologia,
Genova 16163, Italy

Nikos G. Tsagarakis, Darwin G. Caldwell

Advanced Robotics Department,
Istituto Italiano di Tecnologia,
Genova 16163, Italy

Jian S. Dai

King's College London,
University of London, Strand,
London WC2R2LS, UK

Lakmal Seneviratne

Robotics Institute,
Khalifa University of Science, Technology and
Research,
127788, Abu Dhabi, UAE;
King's College London,
University of London, Strand,
London WC2R2LS, UK

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received March 20, 2012; final manuscript received June 7, 2012; published online October 1, 2012. Assoc. Editor: Federico Thomas.

J. Mechanisms Robotics 5(1), 011002 (Oct 01, 2012) (10 pages) Paper No: JMR-12-1034; doi: 10.1115/1.4007492 History: Received March 20, 2012; Revised June 07, 2012

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.

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References

Figures

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Fig. 1

The compliant joint

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Fig. 2

Flow chart for stiffness design of serial compliant manipulators

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Fig. 3

The 3DOF serial compliant manipulator

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Fig. 4

kinematic parameters of the 3DOF serial compliant manipulator (a) the 3DOF manipulator and (b) parameters of link 2 and link 3

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Fig. 5

responded angle change of joint 1 and the impact force (a) responded angle change of joint 1 and (b) impact force

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Fig. 6

Relation to different directions of impact force and joint velocity (a) distance (D1) between end-effector and z-axis and (b) maximum joint 1 torque with variable (q2, q3)

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Fig. 7

The maximum joint torque with variable stiffness

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Fig. 8

Impact results of the 2DOF serial compliant manipulator (a) modulus of projected end-effector point P and (b) loci of joint angle changes

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Fig. 9

Different directions of impact and end-effector velocity (a) different directions of impact and (b) different directions of velocity v

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Fig. 10

The maximum joint torque with different stiffness (a) for joint 2 and (b) for joint 3

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