This is an early draft, need to define the weight of pib, motor torques and speeds
In this document, we outline the features and capabilities required for the knee of Pibpib, our humanoid robot. By understanding these requirements, we can determine the appropriate transmission ratio and method of transmission to ensure effective movement and stability.
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The knee experiences its maximum static torque when pib is in the lowest possible squatting position. Assuming that the knee can bend to the maximum angle of 135°, the torque in this position can be calculated using the following formula:
T\_stat = F \* x*
Where:
F = Force exerted due to the robot's weight
x = Distance from the axis of rotation (lever arm length)
Let's assume:
The mass of Pib pib is 40 kg
Gravitational acceleration g is 9.81 m/s²
Thus:
F = 40 kg \* 9.81 m/s² = 392.4 N*\
x = 0.370 m\
T\_stat = 392.4 N \* 0.370 m = 145.2 Nm*
Since there are two knees, the torque per knee would be 145.2 Nm / 2 = 72.6 Nm for each knee.
To determine the maximum torque the knee should be capable of handling, we consider the scenario where pib is balancing entirely on one knee. In addition, a safety margin must be included to account for dynamic loads and other uncertainties. Let’s assume a safety margin factor of 3.0, which leads to a maximum dynamic torque:
T\_dyn, max = 145.2 Nm \* 3.0 = 435.6 Nm*
Movement Speed
Assuming that pib should be able to stand up from a squatting position within 1 second, we need to calculate the necessary rotational speed for the knee joint. This can be approximated by considering the angular displacement over time. The knee joint should be able to rotate from 135° to 0° in 1 second. We denote the rotational speed as ω (omega) and calculate it as follows:
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To match the required dynamic torque of 435.6 Nm, we will select a suitable transmission ratio r such that:
T\_motor \* r = T\_dyn, max*
Where T\_motor is the torque output of the motor. Depending on the motor specifications, we will choose a transmission ratio that balances both torque requirements and movement speed to achieve the desired performance for the knee joint.
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