Electric motor
The actuator is selected by power. The required value comes from the simulation. Because of the large variety of electric motors, the possibility to connect them to a large amount of different transmissions and the lower costs, compared to linear motors, an electric motor - in this case a brushless DC motor - is used to actuate the demonstrator. To achieve the required values of velocity and force at the mechanical leg, a transmission is necessary. Additionally the rotation of the electric motor has to be converted to a translational movement of the Bowden cable.
The maxima of power, knee torque and angular velocity are not reached at the same time. So motor and transmission are not selected by the maximum power but by the product of maximum knee torque and maximum angular velocity, which is higher than the maximum power. This is necessary because the transmission will not be able to shift between several gears. In reality this requirement is also given because the values which are the basis for the motor selection are extracted from a real human jump and a muscle has also only one transmission between translational contraction and rotational motion of the joint.
The conversion from rotational to translational movement is realized by a spindle, which is de- signed by “item Industrietechnik GmbH”. It is powerful enough to fulfill the requirements from the simulation and fits into the actuation box without any adapters because it has the same shape like the aluminum profiles used for the frame [dat3]. Its transmission ratio is 20 mm/revolution and its stroke is 190 mm.
To select a motor-transmission-combination, the maximum knee torque and angular velocity are calculated to force and translational velocity by the radius of the pulley
;#;
<latex>\begin{align*}
F_{max} &= \frac{M_{max,knee}}{2*r_{sheave}}\\
v_{max} &= \dot{\phi}_{max,knee} * 2r_{sheave}
\end{align*}</latex>
;#;
Afterwards, they are calculated back to torque and angular velocity by the transmission ratio of the spindle, which has the unit m/revolution. The results of this calculation are the required maximum output torque and angular velocity of the transmission.
;#;
<latex>\begin{align*}
M_{trans,out,max} &= \frac{F_{max}*i_{spindle}}{2\pi*\frac{v_{max}}{i_{spindle}}}
\end{align*}</latex>
;#;
The efficiency of the spindle is already known and can be considered as $\eta_{spindle} = 0,85$. The loss resulting from the efficiencies of transmission, translational and rotational bearings, Bowden cable etc. is still unknown and has to be considered using a safety factor which is multiplied to the trans- mission output torque $M_{trans,out,max}$. This safety factor can be estimated as follows:
;#;
<latex>\begin{align*}
S = \tilde{S} \frac{1}{\tilde{\eta}_{trans}} * \frac{1}{\tilde{\eta}_{bowden}} * \frac{1}{\tilde{\eta}_{bearing,rot}} * \frac{1}{\tilde{\eta}_{bearing,trans}}
\end{align*}</latex>
;#;
The efficiency values are shown in the following table.
<imgcaption image1|Estimated efficiencies of powertrain components>
</imgcaption>
Considering the loss of the mechanical components the maximum power of the electric motor has to be
;#;
<latex>\begin{align*}
P_{max,motor} &= S * M_{trans,out,max} * \phi_{trans,out,max}
\end{align*}</latex>
;#;
Using the required maximum power of the electric motor, the maximum output torque and angular velocity a combination of electric motor and transmission can be selected. To simplify selection and design, motor and transmission shafts should fit together without any adapters. This consideration leads to the conclusion that motor and transmission should be from the same company. “Maxon Motor AG” supplies motors and transmissions which fit the requirements. The electric motor is a 200 W direct current motor with a diameter of 30 mm [dat4] and the transmission is a planetary drive with a transmission ratio of 15:1 and maximum efficiency $\eta_{rans} = 0,81$ [dat5].
The next table shows the values required by the simulation outcome and the values reachable by the motor-transmission-spindle-combination considering the known and the estimated efficiency losses ($\eta_{spindle}, \eta_{trans}, \tilde{\eta}_{bowden}, \tilde{\eta}_{bearing,rot}, \tilde{\eta}_{bearing,trans}$).
<imgcaption image2|Required and reachable characteristics of actuation box>
</imgcaption>
The whole process of motor and transmission selection is shown in the following figure.
<imgcaption image2|Development process: motor and transmission selection>
</imgcaption>