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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

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Front. Mech. Eng.    2021, Vol. 16 Issue (4) : 711-725    https://doi.org/10.1007/s11465-021-0647-1
RESEARCH ARTICLE
Mechanical design and analysis of a novel variable stiffness actuator with symmetrical pivot adjustment
Yiwei LIU(), Shipeng CUI, Yongjun SUN
State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China
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Abstract

The safety of human–robot interaction is an essential requirement for designing collaborative robotics. Thus, this paper aims to design a novel variable stiffness actuator (VSA) that can provide safer physical human–robot interaction for collaborative robotics. VSA follows the idea of modular design, mainly including a variable stiffness module and a drive module. The variable stiffness module transmits the motion from the drive module in a roundabout manner, making the modularization of VSA possible. As the key component of the variable stiffness module, a stiffness adjustment mechanism with a symmetrical structure is applied to change the positions of a pair of pivots in two levers linearly and simultaneously, which can eliminate the additional bending moment caused by the asymmetric structure. The design of the double-deck grooves in the lever allows the pivot to move freely in the groove, avoiding the geometric constraint between the parts. Consequently, the VSA stiffness can change from zero to infinity as the pivot moves from one end of the groove to the other. To facilitate building a manipulator in the future, an expandable electrical system with a distributed structure is also proposed. Stiffness calibration and control experiments are performed to evaluate the physical performance of the designed VSA. Experiment results show that the VSA stiffness is close to the theoretical design stiffness. Furthermore, the VSA with a proportional–derivative feedback plus feedforward controller exhibits a fast response for stiffness regulation and a good performance for position tracking.
Keywords variable stiffness actuator      variable stiffness module      drive module      symmetrical structure      double-deck grooves      expandable electrical system     
Corresponding Author(s): Yiwei LIU   
Just Accepted Date: 09 August 2021   Online First Date: 31 August 2021    Issue Date: 28 January 2022
 Cite this article:   
Yiwei LIU,Shipeng CUI,Yongjun SUN. Mechanical design and analysis of a novel variable stiffness actuator with symmetrical pivot adjustment[J]. Front. Mech. Eng., 2021, 16(4): 711-725.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0647-1
https://academic.hep.com.cn/fme/EN/Y2021/V16/I4/711
Fig.1  Design principle of variable stiffness module.
Fig.2  Schematic of the stiffness adjustment principle. (a) Geometrical analysis; (b) force analysis.
Fig.3  Analysis of Archimedean spiral cam. (a) Archimedean spiral line; (b) force analysis.
Fig.4  Maximum flexible deformation angle versus pivot position.
Fig.5  Theoretical characteristics of VSA: (a) elastic torque, (b) stiffness, (c) elastic energy, and (d) resistance torque.
Fig.6  Design of the VSA. (a) CAD model of the VSA; (b) prototype of the VSA.
Fig.7  CAD model of the drive module. (a) Section view; (b) side view.
Fig.8  CAD model of the variable stiffness module. (a) Side view 1; (b) side view 2; and (c) explosive view.
Fig.9  Prototype of the variable stiffness module.
Fig.10  Framework of the electrical system.
Fig.11  Hardware of the controller: (a) central controller, (b) actuator controller.
Fig.12  Experimental platform for stiffness calibration.
Fig.13  Stiffness calibrate results of the VSA.
Fig.14  Experimental platform for stiffness motor response and tracking.
Fig.15  Step response for stiffness motor: (a) adjusting stiffness from infinity to zero, (b) adjusting stiffness from zero to infinity.
Fig.16  Tracking experiments: (a) different loads, (b) different stiffnesses, and (c) different frequencies.
Name RoS/(N·m·rad ?1) RST/s RoM/(° ) NT/(N·m) PT/(N·m) Mass/kg Size/(mm×mm) Modular Brake
FSJ [ 29] 52.4–826 0.33 0–180 31.3 67 1.41 94×118 No No
MACCEPA [ 27] 5–110 10.00 0–300 40 70 2.4 / No No
vsaUT-II [ 34] 0.7–948 0.90 0–57.2 21.8 60 2.5 / No No
S 3VSA [ 30] 12.12?∞ 0.10 0–360 7.6 22.7 1.54 118×125 No No
CompAct-VSA [ 36] 0–∞ 0.10 0–360 / 117 1 120×160 No No
AwAS-II [ 37] 0–∞ 5.00 0–165 / 80 1.1 140×180 No No
SVSA [ 31] 1.7–150.56 0.60* 0–360 9.46 22.1 2.4 / No No
SVSA-II [ 41] 0–∞ 0.30* 0–360 / 25 1.647 / No No
Proposed VSA 0– ∞ 0.40 0–360 36 68 2.46 104×156 Yes Yes
Tab.1  Comparisons of different VSAs
Abbreviations
cPCI Compact peripheral component interconnect
VSA Variable stiffness actuator
DSP Digital signal processor
FPGA Field programmable gate array
HIT Harbin Institute of Technology, China
Variables
a Vertical distance from the pivot to the spring axis
Α Angle between the lever and the output link
b Distance between the spring axis and the symmetrical center line of the variable stiffness module
c Polar radius per polar angle
d Polar radius when ρ = 0
e 1, e 2 Position error, e 1 = θ 1 ? θ 1d, e 2 = θ 2 – θ 2d
E Stored elastic energy
f p Force applied by the pivot on the Archimedean spiral cam, f p = ? F p
f pa Decomposed of f p along the direction perpendicular to the spring axis
f pat Decomposed of f pa along the direction perpendicular to the tangent of the Archimedean spiral line
  
F e Elastic force of the VSA generated at the force point in the opposite direction of load force F l
F l Load force applied at the force point
F lt Decomposed along the direction perpendicular to the lever
F p Force applied on the lever from the pivot
F pa Decomposed along the direction perpendicular to the spring axis
F s Spring force
F st Decomposed along the direction perpendicular to the lever
g Gravity term
k Spring stiffness
k 1p, k 1d Proportional and derivative coefficients of control command u 1, respectively
k 2p, k 2d Proportional and derivative coefficients of control command u 2, respectively
K Stiffness of the VSA
l Total length of the lever
l 1, l 2 Distances from the pivot to the spring point and the force point, respectively
q Link-side position
q d Desired position for link
r Arm of the force f pat relative to the coordinate origin
R Total length of the output link, i.e., the distance between the force point and the center of the variable stiffness module
S Curvature of the Archimedean spiral line at P( x, y)
S 1 Slope between point P( x, y) and the coordinate origin
u 1, u 2 Control commands of the principal and stiffness motors, respectively
? x Deformation of the spring
β Angle between the force f pa and the tangent of the Archimedean spiral line
γ Angle between the lever and the linear groove of the input link
τ 1 Load torque exerted on the output link
τ e Elastic torque of the variable stiffness module
τ r Resistance torque
θ 1, θ 2 Principal and stiffness motor positions, respectively
θ 1d, θ 2d Desired positions for the principal and stiffness motors, respectively
φ Angle between the input link and the output link that represents the flexible deformation angle of the VSA
ρ Polar angle of point P( x, y) on the Archimedean spiral line
  
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