# Estimation of the motion parameters of a platform

## Contents |

### Linear motion speed

The diameter of a platform wheel is D=140 mm. The length of wheel circumference is L=π·D=439.81mm. The maximal motor speed is w_{motor}=5200 rpm. The gear ratio is q=100:1. The maximal output shaft speed of a gearbox, which is also a wheel speed is w_{shaft}=w_{motor}/q=5200/100=52 rpm = 52/60 rotations/sec. The path S, which wheel can move for one second is equal S=w_{shaft}*L = 381.1688 mm = 0.38116 meters. Velocity is S/t (t = 1 second), V = 0.38116 m/s = 1.37216 km/h.

- Maximal linear speed: V = 0.38116 m/s

### Wheel rotation speed

The same motor system with rotation speed w_{shaft} is rotating each wheel. Hence, the maximal rotation speed is w_{shaft}*2*π = 5.445427 rad/second = 312°/second.

- Maximal rotation speed: w
_{shaft}= 5.445427 rad/s = 312°/s.

In normal conditions a single wheel will not change direction on more than [-45°,+90°], hence the maximal rotation degree is 90-(-45)= 135°. Hence, maximal time required for each wheel position is (135/312) seconds = 0.433 s.

- Wheel positioning time: T
_{pos}≤ 0.433 s (at maximal motor speed).

## Motion modes

### Linear motion

#### Longitudinal mode

Below is the illustration of the straight (longitudinal, forward and backward) motion process. Top view:

#### Lateral mode

Below is the illustration of the lateral motion process. Top view:

### Rotation

Below is the illustration of the platform rotation process. Top view:

### Spline follow mode **(Incorrect)**

**Todo: This design is incorrect! For history only. **

Below is the illustration of how a spline trajectory can be followed. Top view: