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.

References

References
1.
Vischer
,
D.
, and
Kathib
,
O.
,
1995
, “
Design and Development of High Performance Torque-Controlled Joints
,”
IEEE Trans. Rob. Autom.
,
11
, pp.
537
544
.10.1109/70.406938
2.
Sang-Ho
,
H.
,
Hale
,
J. G.
, and
Cheng
,
G.
,
2007
, “
Full-Body Compliant Human–Humanoid Interaction: Balancing in the Presence of Unknown External Forces
,”
IEEE Trans. Rob. Autom.
,
23
(
5
), pp.
884
898
10.1109/TRO.2007.904896.
3.
Pratt
,
G.
, and
Williamson
,
M.
,
1995
, “
Series Elastic Actuators
,”
Proceedings of the 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems
, Vol. 1, pp.
399
406
.
4.
Tonietti
,
G.
,
Schiavi
,
R.
, and
Bicchi
,
A.
,
2005
, “
Design and Control of a Variable Stiffness Actuator for Safe and Fast Physical Human/Robot Interaction
,”
International Conference on Robotics and Automation
,
Barcelona
,
Spain
.
5.
Wolf
,
S.
, and
Hirzinger
,
G.
,
2008
, “
A New Variable Stiffness Design: Matching Requirements of the Next Robot Generation
,”
IEEE International Conference on Robotics and Automation
, pp.
1741
1746
.
6.
Tsagarakis
,
N. G.
,
Laffranchi
,
M.
,
Vanderborght
,
B.
, and
Caldwell
,
D. G.
,
2009
, “
A Compact Soft Actuator for Small Scale Robotic Systems
,”
International Conference on Robotics and Automation
,
Kobe
,
Japan
.
7.
Curran
,
S.
,
Knox
,
B. T.
,
Schmiedeler
,
J. P.
, and
Orin
,
D. E.
,
2009
, “
Design of Series-Elastic Actuators for Dynamic Robots with Articulated Legs
,”
ASME J. Mech. Rob.
,
1
(
1
), p.
011006
.10.1115/1.2960535
8.
Morrel
,
J. B.
,
1996
, “
Parallel Coupled Micro-Macro Actuators
,” Ph.D. thesis,
Massachusetts Institute of Technology
,
Cambridge, MA
.
9.
Shin
,
D.
,
Sardellitti
,
I.
, and
Khatib
,
O.
,
2008
, “
A Hybrid Actuation Approach for Human-Friendly Robot Design
,”
Proceedings of the 2008 IEEE International Conference on Robotics and Automation
.
10.
Semini
,
C.
,
Tsagarakis
,
N. G.
,
Vanderborght
,
B.
,
Yang
,
Y. S.
, and
Caldwell
,
D. G.
,
2008
, “
HyQ—Hydraulically Actuated Quadruped Robot: Hopping Leg Prototype
,”
IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob)
, pp.
593
599
.
11.
Su
,
H. J.
,
Dorozhkin
,
D. V.
, and
Vance
,
J. M.
,
2009
, “
A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
4
), p.
041009
.10.1115/1.3211024
12.
Pei
,
X.
,
Yu
,
J. J.
,
Zong
,
G. H.
,
Bi
,
S. S.
, and
Hu
,
Y. D.
,
2009
, “
A Novel Family of Leaf-Type Compliant Joints: Combination of Two Isosceles-Trapezoidal Flexural Pivots
,”
ASME J. Mech. Rob.
,
1
(
2
), p.
021005
.10.1115/1.3046140
13.
Su
,
H. J.
, and
McCarthy
,
J. M.
,
2007
, “
Synthesis of Bistable Compliant Four-Bar Mechanisms Using Polynomial Homotopy
,”
ASME J. Mech. Des.
,
129
(
10
), pp.
1094
1098
.10.1115/1.2757192
14.
Kim
,
C.
,
2009
, “
Design Strategies for the Topology Synthesis of Dual Input-Single Output Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
4
), p.
041002
.10.1115/1.3204252
15.
Azadi
,
M.
,
Behzadipour
,
S.
, and
Faulkner
,
G.
,
2010
, “
Variable Stiffness Spring Using Tensegrity Prisms
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
041001
.10.1115/1.4001776
16.
Demirel
,
B.
,
Emirler
,
M. T.
,
Sönmez
,
Ümit
, and
Yörükoğlu
,
A.
,
2010
, “
Semicompliant Force Generator Mechanism Design for a Required Impact and Contact Forces
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
045001
.10.1115/1.4002076
17.
Krishnan
,
G.
,
Kim
,
C.
, and
Kota
,
S.
,
2011
, “
An Intrinsic Geometric Framework for the Building Block Synthesis of Single Point Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
3
(
1
), p.
011001
.10.1115/1.4002513
18.
Chen
,
G. M.
,
Aten
,
Q. T.
,
Zirbel
,
S.
,
Jensen
,
B. D.
, and
Howell
,
L. L.
,
2010
, “
A Tristable Mechanism Configuration Employing Orthogonal Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
2
(
1
), p.
014501
.10.1115/1.4000529
19.
Wang
,
M. Y.
,
2009
, “
A Kinetoelastic Formulation of Compliant Mechanism Optimization
,”
ASME J. Mech. Rob.
,
1
(
2
), p.
021011
10.1115/1.3056476.
20.
Deepak
,
S. R.
,
Dinesh
,
M.
,
Sahu
,
D. K.
, and
Ananthasuresh
,
G. K.
,
2009
, “
A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
1
), p.
011003
.10.1115/1.2959094
21.
Zhou
,
H.
, and
Mandala
,
A. R.
,
2012
, “
Topology Optimization of Compliant Mechanisms Using the Improved Quadrilateral Discretization Model
,”
ASME J. Mech. Rob.
,
4
(
2
), p.
021007
.10.1115/1.4006194
22.
Banerjee
,
A.
,
Bhattacharya
,
B.
, and
Mallik
,
A. K.
,
2011
, “
Forward and Inverse Analyses of an SMA Actuated Compliant Link
,”
ASME J. Mech. Rob.
,
3
(
2
), p.
021003
.10.1115/1.4003528
23.
Su
,
H. J.
,
2011
, “
Mobility Analysis of Flexure Mechanisms via Screw Algebra
,”
ASME J. Mech. Rob.
,
3
(
4
), p.
041010
.10.1115/1.4004910
24.
Ghafoor
,
A.
,
Dai
,
J. S.
, and
Duffy
,
J.
,
2004
, “
Stiffness Modelling of a Soft-Finger Contact in Robotic Grasping
,”
ASME J. Mech. Des.
,
126
(
4
), pp.
646
656
.10.1115/1.1758255
25.
Hoetmer
,
K.
,
Woo
,
G.
,
Kim
,
C.
, and
Herder
,
J.
,
2010
, “
Negative Stiffness Building Blocks for Statically Balanced Compliant Mechanisms: Design and Testing
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
041007
.10.1115/1.4002247
26.
Quennouelle
,
C.
, and
Gosselin
,
C.
,
2009
, “
A Quasi-Static Model for Planar Compliant Parallel Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
2
), p.
021012
.10.1115/1.3046144
27.
Wang
,
W. J.
, and
Yu
,
Y. Q.
,
2010
, “
New Approach to the Dynamic Modeling of Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
2
(
2
), p.
021003
.10.1115/1.4001091
28.
Briot
,
S.
, and
Arakelian
,
V.
,
2010
, “
On the Dynamic Properties of Rigid-Link Flexible-Joint Parallel Manipulators in the Presence of Type 2 Singularities
,”
ASME J. Mech. Rob.
,
2
(
2
), p.
021004
.10.1115/1.4001121
29.
Ding
,
X.
, and
Dai
,
J. S.
,
2008
, “
Characteristic Equation-Based Dynamics Analysis of Vibratory Bowl Feeders With Three Spatial Compliant Legs
,”
IEEE Trans. Autom. Sci. Eng.
,
5
(
1
), pp.
164
175
.10.1109/TASE.2007.910301
30.
Ma
,
O.
, and
Wang
,
J. G.
,
2007
, “
Model Order Reduction for Impact-Contact Dynamics Simulations of Flexible Manipulators
,”
Robotica
,
25
, pp.
397
407
.10.1017/S026357470600316X
31.
Dai
,
J. S.
, and
Ding
,
X. L.
,
2006
, “
Compliance Analysis of a Three-Legged Rigidly-Connected Platform Device
,”
Trans. ASME J. Mech. Des.
,
128
(
4
), pp.
755
764
.10.1115/1.2202141
32.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2009
, “
Synthesis of Multi-Degree of Freedom, Parallel Flexure System Concepts Via Freedom and Constraint Topology (FACT)—Part I: Principles
,”
Precis. Eng.
,
34
, pp.
259
270
.10.1016/j.precisioneng.2009.06.008
33.
Bicchi
,
A.
, and
Tonietti
,
G.
,
2004
, “
Fast and Soft Arm Tactics: Dealing With the Safety-Performance Trade-Off in Robot Arms Design and Control
,”
IEEE Rob. Autom. Mag.
,
11
, pp.
22
33
.10.1109/MRA.2004.1310939
34.
Haddadin
,
S.
,
Albu-Schäffer
,
A.
, and
Hirzinger
,
G.
,
2007
, “
Safety Evaluation of Physical Human-Robot Interaction via Crash-Testing
,”
Science and Systems Conference (RSS2007) on Robotics
.
35.
Luca
,
A. D.
,
Albu-Schäffer
,
A.
,
Haddadin
,
S.
, and
Hirzinger
,
G.
,
2006
, “
Collision Detection and Safe Reaction With the DLR-III Lightweight Manipulator Arm
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, pp.
1623
1630
.
36.
Kazuo
,
Hirai
,
Masato
,
Hirose
,
Yuji
Haikawa
, and
Toru
Takenaka
,
1998
, “
The Development of Honda Humanoid Robot
,”
International Conference on Robotics and Automation
, pp.
1321
1326
.
37.
Jerry
,
P.
, and
Gill
,
P.
,
1998
, “
Intuitive Control of a Planar Bipedal Walking Robot
,”
International Conference on Intelligent Robots and Systems
, pp.
2014
2021
.
38.
Tonietti
,
G.
,
Schiavi
,
R.
, and
Bicchi
,
A.
,
2005
, “
Design and Control of a Variable Stiffness Actuator for Safe and Fast Physical Human/Robot Interaction
,”
Proceedings of the IEEE
,
International Conference on Robotics and Automation
, pp.
526
531
.
39.
Hollander
,
K. W.
,
Sugar
,
T. G.
, and
Herring
,
D. E.
,
2005
, “
A Robotic ‘Jack Spring' For Ankle Gait Assistance
,”
Proceedings CIE 2005
,
ASME 2005 International Design Engineering Technical Conferences 2005
,
California
, pp.
24
28
.
40.
Laffranchi
,
M.
,
Tsagarakis
,
N. G.
, and
Caldwell
,
D. G.
,
2012
, “
Analysis and Development of a Semiactive Damper for Compliant Actuation Systems
,”
IEEE/ASME Trans. Mechatron
., PP(99), pp.
1
10
.
41.
Dai
,
J. S.
, and
Zhao
,
T. S.
,
2002
, “
Stiffness Characteristics and Kinematics Analysis of Two-Link Elastic Underactuated Manipulators
”.
J. Rob. Syst.
,
19
(
4
), pp.
169
176
.10.1002/rob.10031
42.
Zhao
,
T. S.
, and
Dai
,
J. S.
,
2003
, “
Dynamics and Coupling Actuation of Elastic Underactuated Manipulators
,”
J. Rob. Syst.
,
20
(
3
), pp.
135
146
.10.1002/rob.10075
43.
Shin
,
D.
,
Seitz
,
F.
,
Khatib
,
O.
, and
Cutkosky
,
M.
,
2010
, “
Analysis of Torque Capacities in Hybrid Actuation for Human-Friendly Robot Design
,”
Proceedings of the 2010 IEEE International Conference on Robotics and Automation
,
Anchorage
,
Alaska
, May 3–8, pp.
799
804
.
44.
Uemaura
,
M.
, and
Kawamura
,
S.
,
2009
, “
Resonance-Based Motion Control Method for Multi-Joint Robot Through Combining Stiffness Adaptation and Iterative Learning Control
,”
Proceedings of the 2009 IEEE International Conference on Robotics and Automation
,
Kobe
,
Japan
, May 12–17, pp.
1543
1548
.
45.
Owen
,
W.
,
Croft
,
E.
, and
Benhabib
,
B.
,
2008
, “
Stiffness Optimization for Two-Armed Robotic Sculpting
,”
Ind. Rob.: Int. J.
,
35
(
1
), pp.
46
57
.10.1108/01439910810843289
46.
Gan
,
D. M.
,
Tsagarakis
,
N. G.
,
Dai
,
J. S.
, and
Caldwell
,
D. G.
,
2011
, “
Joint Stiffness Tuning for Compliant Robots: Protecting the Robot Under Accidental Impacts
,” IFToMM 13th World Congress in Mechanism and Machine Science,
Guanajuato
,
Mexico
, June 19–25.
47.
Gilardi
,
G.
, and
Sharf
,
I.
,
2002
, “
Literature Survey of Contact Dynamics Modelling
,”
Mech. Mach. Theory
,
37
, pp.
1213
1239
.10.1016/S0094-114X(02)00045-9
48.
Vukobratovic
,
M.
, and
Potkonjak
,
V.
,
1999
, “
Dynamics of Contact Tasks in Robotics. Part I: General Model of Robot Interacting With Environment
,”
Mech. Mach. Theory
,
34
, pp.
923
942
.10.1016/S0094-114X(97)00091-8
49.
Dormand
,
J. R.
,
1996
,
Numerical Methods for Differential Equations: A Computational Approach
,
CRC Press
,
Boca Raton, FL
.
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