QB Robotics qbmove Advanced Kit, User Manual

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15
28 aprile 2021
Moreover, also considering the motors’ speed, our actuator has a 3d workspace. The figures
below show the Torque
–
Speed characteristic (Figure 3-13) and the VSA workspace (Figure
3-14).
Figure 3-13 Torque - Speed characteristic.
Figure 3-14 Torque - Speed - Stiffness Workspace.
3.2.2 Mathematical model
The following mathematical functions and their parameters describe the mathematical model of
our agonistic/antagonistic VSA.
equilibrium point
𝑿
𝒆
=
(𝒒
𝟏
+ 𝒒
𝟐
)
𝟐
output stiffness
𝜎 = 𝑎
1
𝑘
1
cosh(𝑎
1
(𝑥 − 𝑞
1
)) + 𝑎
2
𝑘
2
cosh⁡(𝑎
2
(𝑥 − 𝑞
2
))
output torque
𝜏 = 𝑘
1
sinh(𝑎
1
(𝑥
− 𝑞
1
)) + 𝑘
2
sinh(𝑎
2
(𝑥 − 𝑞
2
))
elastic energy
𝐻 =
𝑘
1
(cosh(𝑎
1
(𝑥 − 𝑞
1
)) − 1)
𝑎
1
+
𝑘
2
(cosh(𝑎
2
(𝑥 − 𝑞
2
)) − 1)
𝑎
2
value Unit
k
1
0,0026 [Nm]
a
1
8.9995 [1/rad]
k
2
0.0011 [Nm]
a
2
8.9989 [1/rad]