a novel design of variable stiffness linkage with distributed leaf springs for robots
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Transcript of a novel design of variable stiffness linkage with distributed leaf springs for robots
ICIEA 2013June 19-21, 2013
Xingming Wu, Zijian Zhao, Jianhua Wang*, Dong Xu, Weihai Chen
School of Automation Science and Electrical Engineering
Beihang University, Beijing, China
A Novel Design of Variable Stiffness Linkage with
Distributed Leaf Springs
ICIEA 2016June.5. 2016
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
2 Contents
Introduction1
Design of VSL 2
Stiffness Model of VSL3
Conclusions and Future Work4
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
3 Contents
IntroductionIntroduction1
Design of VSL 2
Stiffness Model of VSL3
Conclusions and Future Work4
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
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.
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
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
7 Introduction - Significance
Conclude the Significance
Safety Assurance Stability Improvement Energy Conservation
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.
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
9 Introduction – Related Works Antagonistic-Controlled Stiffness
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.
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.
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.
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
13
Introduction – Related WorksStructure-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)
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
14
Introduction – Related Works
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.
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
16 Contents
Introduction1
Design of VSL Design of VSL 2
Stiffness Model of VSL3
Conclusions and Future Work4
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
17Design 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)
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
18Design of VSL - Concept of VSL
Vertical Principle Structure Control Stiffness
The vertical principle is realized by applying screw-slider-linkage-slider mechanism
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
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
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
21Design of VSL
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
22Design of VSL
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
23 Contents
Introduction1
Design of VSL 2
Stiffness Model of VSLStiffness Model of VSL3
Conclusions and Future Work4
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
24Stiffness Model of VSL
The deflection of each leaf spring is given as :3
3FlwEI
3
12abI
0
sin wR l
03
3 ( )sin
EI R lF
l
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
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
25Stiffness 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 l
3 20
3
3 ( ) sin4
Eab R ll
K
3 20
3
3 ( ) sin4
Eab R lKl
3 20
3
3 ( )4
Eab R lK
l
3
3FlwEI
0
sin wR l
03
3 ( )sin
EI R lF
l
(1) (2) (3)
(4)
(5)
(6)
(7)
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
26Stiffness 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:
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
27Stiffness Model of VSL
3 20
3
3 ( ) sin4
Eab R ll
(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)
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
28Stiffness Model of VSL
Torsional stiffness (K) for different effective length (l).
3 20
3
3 ( )4
Eab R lKl
(7) τ = f (θ , l)
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
29 Contents
Introduction1
Design of VSL 2
Stiffness Model of VSL3
ConclusionsConclusions4
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
30Conclusion
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
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
31 Contents
Introduction1
Design of VSL 2
Stiffness Model of VSL3
Conclusions and Future WorkConclusions and Future Work4
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
32Conclusion 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
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
33Conclusion and Future Work
Provide the variable stiffness joint to some specific.
Future Work
A Novel Design of Variable Stiffness Linkage (VSL) with Distributed Leaf Springs
34Conclusion and Future Work
Provide the variable stiffness joint to some specific.
Future Work
ICIEA 2013June 19-21, 2013
ICIEA 2016June.5. 2016
THANKS FOR YOUR ATTENTION