a novel design of variable stiffness linkage with distributed leaf springs for robots

1. ICIEA 2013
June 19-21, 2013
Xingming Wu, Zijian Zhao, Jianhua Wang*, Dong Xu, Weihai Chen
School of Automation Science and Electrical Engineering
Beihang University, Beijing, China
zhaozijianzzj@gmail.com
A Novel Design of Variable Stiffness Linkage with
Distributed Leaf Springs
ICIEA 2016
June.5. 2016

2. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
2
Contents
Introduction1
Design of VSL2
Stiffness Model of VSL3
Conclusions and Future Work4

3. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
3
Contents
IntroductionIntroduction1
Design of VSL2
Stiffness Model of VSL3
Conclusions and Future Work4

4. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
4
Introduction - Significance - Safety Assurance
Physical human-robot interaction
inevitably occurs in applications
such as service robots, wearable
robots and rehabilitation robots

5. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
5
Introduction - Significance - Stability Improvement
Rigid joint can only transmit constant stiffness and may results in system
vibration;
While variable stiffness device have relatively flexible terminals that have
adjustable stiffness. Variable stiffness device is often applied to damp out
the undesirable vibration and ensure the dynamic stability.

6. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
6
Introduction - Significance - Energy Conservation
In addition, variable stiffness devices similar to muscles, are
also beneficial to system energy efficiency. During the
execution of the periodic motions, part of kinetic energy will
be temporarily transformed and reserved as elastic potential
one. Later, the energy will be turned back in the next cycle.
As a consequence, in the long run, the whole system will
reduce the energy consumption and improve the propulsive
efficiency by a considerable amount.
Furthermore, it has been proved by many researchers that
energy would be effectively saved by adjusting the nature
frequency of the link to match the actual one during the
specific motion, while the nature frequency is determined by
the link’s inertia and stiffness
Nature Frequency
Motion Frequency

7. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
7
Introduction - Significance
Conclude the Significance
 Safety Assurance
 Stability Improvement
 Energy Conservation

8. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
8
Introduction – Related Works
 Equilibrium-Controlled Stiffness
 G. A. Pratt and M. M. Williamson, ‘‘Series elastic actuators,’’ in Proc. IEEE Int.
Workshop on Intelligent Robots and Systems (IROS’95), Pittsburg, USA, 1995, pp.
399–406.

9. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
9
Introduction – Related Works
 Antagonistic-Controlled Stiffness

10. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
10
Introduction – Related Works
 Antagonistic-Controlled Stiffness
 Migliore S, Brown E, DeWeerth S P. Biologically inspired joint stiffness control[C]//
Robotics and Automation, 2005. ICRA 2005. Proceedings of the 2005 IEEE
International Conference on. IEEE, 2005: 4508-4513.

11. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
11
Introduction – Related Works
 Antagonistic-Controlled Stiffness
 Tonietti G, Schiavi R, Bicchi A. Design and control of a variable stiffness actuator for
safe and fast physical human/robot interaction[C]//Robotics and Automation, 2005.
ICRA 2005. Proceedings of the 2005 IEEE International Conference on. IEEE, 2005:
526-531.

12. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
12
Introduction – Related Works
 Antagonistic-Controlled Stiffness
(b)
 (a) J. W. Hurst, J. Chestnutt, and A. Rizzi, ‘‘An actuator with mechanically adjustable
series compliance,’’ Carnegie Mellon Univ., USA,CMU-RI-TR-04-24, Apr. 2004.
 (b) Thorson I et al. Design considerations for a variable stiffness actuator in a robot
that walks and runs[C]//Proceedings of the Robotics and Mechatronics Conference
(RoboMec). 2007: 1-4.

13. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
13
Introduction – Related Works
Structure-Controlled Stiffness
 Jafari A, et al. A novel actuator with adjustable stiffness (AwAS)[C]//(IROS 2010)
 AwAS-II: A New Actuator with Adjustable Stiffness based on the Novel Principle of
Adaptable Pivot point and Variable Lever ratio[C]// (ICRA 2011)

14. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
14
Introduction – Related Works

15. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
15
Introduction
Special Points in My Work
 However, products mentioned above are almost can only be used in actuated
joints but can hardly act as a middle link to make the stiffness of original segment
adjustable.
 In this paper, we introduce a novel variable stiffness linkage (VSL) with distributed
leaf springs, which is designed in the conception of structure controlled stiffness to
save the energy from holding the stiffness. In addition, as the position control part
and the stiffness control part are designed separately, the position control part is
optional according to the specific application occasions.

16. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
16
Contents
Introduction1
Design of VSLDesign of VSL2
Stiffness Model of VSL3
Conclusions and Future Work4

17. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
17
Design of VSL - Concept of VSL
 Vertical Principle
 The source power to adjust the stiffness should be vertical to the force generated by
the elastic element.
 Only then the extra energy to counteract the force from the elastic deformation could
be saved.
Direction of the force
from elastic deformation
Direction of the force
to adjust the stiffness
(1)
(2)
(3)
(4)

18. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
18
Design of VSL - Concept of VSL
 Vertical Principle
 Structure Control Stiffness
 The vertical principle is realized by applying screw-slider-linkage-slider mechanism

19. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
19
Design of VSL - Two Scheme for Selection
(a) Case of the spring set at the rim
(b) Case of the spring set at the middle of the joint
(c) Force distribution of the two cases

20. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
20
Design of VSL - Two Scheme for Selection
(a) Design of VSL (b) Mechanical realization of VSL

21. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
21
Design of VSL

22. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
22
Design of VSL

23. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
23
Contents
Introduction1
Design of VSL2
Stiffness Model of VSLStiffness Model of VSL3
Conclusions and Future Work4

24. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
24
Stiffness Model of VSL
 The deflection of each leaf spring is given as :
3
3
Fl
w
EI
=
3
12
ab
I =
0
sin
w
R l
θ =
+
0
3
3 ( )
sin
EI R l
F
l
θ
+
=
 Where E is the Young’s modulus of the leaf spring and I is the inertia moment of cross section relative to the
neutral axis. If the leaf spring’s width is a and the thickness is b, I can be described as :
 The relation between the bending leaf spring and the torsional joint is :
 Then the force applied to the leaf spring could be de-scribed by the effective length of the leaf spring (l) and the torsional angle
(θ):
(3)
(2)
(1)
(a) Schematic of slider and leaf springs (b) measurement of slider and leaf spring model

25. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
25
Stiffness Model of VSL
 Considering the little change of the direction of F and distributed three leaf springs in parallel, moment equation is approximated as:
 Substitute formula (3) into formula (4), we can get the torque as the function of
l and θ:
 Torsional stiffness can be calculated by the formula so the torsional stiffness k is also the function of l
and θ:
 In practical application, the torsional angle θ would less
than 10°, so considering approximation , torsional
stiffness k could be formulated as:
03 ( )F R lτ = +
3 2
0
3
3 ( )
sin
4
Eab R l
l
τ θ
+
=
K
τ
θ
= 3 2
0
3
3 ( ) sin
4
Eab R l
K
l
θ
θ
+
=
3 2
0
3
3 ( )
4
Eab R l
K
l
+
=
3
3
Fl
w
EI
=
0
sin
w
R l
θ =
+
0
3
3 ( )
sin
EI R l
F
l
θ
+
=(1) (2) (3)
(4)
(5)
(6)
(7)

26. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
26
Stiffness Model of VSL
Table.1 Model parameters for the VSL
Parameter unit value
E GPa 206
a mm 6
b mm 0.5
R0 mm 23
lmin mm 2.5
lmax mm 24.5
θmin ° 0
θmax ° 10
 For the prototype of VSL, parameters of each components is measured as follows:

27. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
27
Stiffness Model of VSL
3 2
0
3
3 ( )
sin
4
Eab R l
l
τ θ
+
=
(a) Torque for different effective length of the leaf
spring (l) and the torsional angle (θ)
(b) Effect of effective length (l) on the torque for
discrete values of the torsional angle (θ)
(c) Effect of torsional angle (θ) on the torque for
discrete values of the effective length (l)
(a)
(b) (c)
(5)τ = f (θ , l)

28. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
28
Stiffness Model of VSL
Torsional stiffness (K) for different
effective length (l).
3 2
0
3
3 ( )
4
Eab R l
K
l
+
= (7)τ = f (θ , l)

29. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
29
Contents
Introduction1
Design of VSL2
Stiffness Model of VSL3
ConclusionsConclusions4

30. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
30
Conclusion
 In this paper, a novel variable stiffness linkage (VSL) with distributed leaf springs is designed to help achieving safety assurance, stability improvement and energy conservation
in robots and mechanical applications.
 By using a screw-slider-linkage-slider mechanism and applying the symmetry conception, VSL could work stably and effectively. By building an effective stiffness model, VSL
could be widely used in applications where stiffness is expected to be controlled.
 From the simulation result, it verifies the effectiveness of the VSL that the stiffness could be effectively controlled with in the expected range from 18 N/m to more than 1000
N/m.
 Conclusion

31. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
31
Contents
Introduction1
Design of VSL2
Stiffness Model of VSL3
Conclusions and Future WorkConclusions and Future Work4

32. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
32
Conclusion and Future Work
 In this paper, a novel variable stiffness linkage (VSL) with distributed leaf springs is designed to help achieving safety assurance, stability improvement and energy conservation
in robots and mechanical applications.
 By using a screw-slider-linkage-slider mechanism and applying the symmetry conception, VSL could work stably and effectively. By building an effective stiffness model, VSL
could be widely used in applications where stiffness is expected to be controlled.
 From the simulation result, it verifies the effectiveness of the VSL that the stiffness could be effectively controlled with in the expected range from 18 N/m to more than 1000
N/m.
 Conclusion

33. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
33
Conclusion and Future Work
 Provide the variable stiffness joint to some specific.
 Future Work

34. A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
34
Conclusion and Future Work
 Provide the variable stiffness joint to some specific.
 Future Work

35. ICIEA 2013
June 19-21, 2013
ICIEA 2016
June.5. 2016
THANKS FOR YOUR ATTENTION