Given an example of a coordinated move, such as:
Specifying a feedrate of 10 units/sec would cause the motion of all three axes to complete within 10 seconds.
The velocity of each axis is calculated individually as follows:
Calculate the Vector (v) Magnitude
First, the magnitude of the position vector is calculated. This is given by
In this example, we will assume that the axes start at a position of XYZ (0,0,0). Hence, the magnitude of vector |v| would be:
Determine the Vector Component Angles
Using the vector magnitude, the angles α, β, and γ can be calculated.
Imagining each angle as its own right-angle triangle, the angle is given by the inverse cosine:
Calculate the Velocity Vector Components
Given the angles for each component, the velocity of each can be calculated based on the magnitude of the vector feedrate.
For a coordinated feedrate of 10 units/s, the individual axis components are as follows:
Final Equation
Ultimately, this boils down to the following equation:
Where
CoordinatedFeedrate is the feedrate specified to the coordinated command.
ComponentDistance is the distance the axis in question will travel during the move.
Axis1Distance is the distance the first axis will travel during the move.
Axis2Distance is the distance the second axis will travel during the move.
Axis3Distance is the distance the third axis will travel during the move.