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.
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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
- a :
-
Vertical distance from the pivot to the spring axis
- A :
-
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, e1 = θ1 − θ1d, e2 = θ2 − θ2d
- E :
-
Stored elastic energy
- f p :
-
Force applied by the pivot on the Archimedean spiral cam, fp = − Fp
- f pa :
-
Decomposed of fp along the direction perpendicular to the spring axis
- f pat :
-
Decomposed of fpa 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 F1
- F 1 :
-
Load force applied at the force point
- F lt :
-
Decomposed along the direction perpendicular to the lever
- Fp:
-
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 u1, respectively
- k 2p, k 2d :
-
Proportional and derivative coefficients of control command u2, 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 fpat 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
- Δx :
-
Deformation of the spring
- β :
-
Angle between the force fpa 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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Acknowledgement
This work was supported by the National Key R&D Program of China (Grant No. 2017YFB1300400) and the National Natural Science Foundation of China (Grant No. 51805107).
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Liu, Y., Cui, S. & Sun, Y. Mechanical design and analysis of a novel variable stiffness actuator with symmetrical pivot adjustment. Front. Mech. Eng. 16, 711–725 (2021). https://doi.org/10.1007/s11465-021-0647-1
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DOI: https://doi.org/10.1007/s11465-021-0647-1