Equations for Traditional Motion-Laws

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Equations for Traditional Motion-Laws

Motion-law Equations

We evaluate exact values of Position, Velocity, Acceleration, and Jerk values for each motion-law from the equation for each motion-derivative.


Motion-Laws

The important motion-laws are:

•Dwell

•Constant Velocity

•Constant Acceleration - Constant Deceleration

•Simple Harmonic Motion

•Cycloidal

•Polynomial 2-3

•Polynomial 3-4-5

•Polynomial 4-5-6-7

•Modified Sinusoid

•Modified Trapezoid


Motion Functions

Actual Velocity, Acceleration, and Jerk

You can calculate the actual motion-values for each motion-derivative of each motion-law if you know the actual total displacement ( ), and the actual total (time) period ( ).

Actual Position =

 

Actual Velocity =

 

Actual Acceleration =

 

Actual Jerk =

 

is known maximum displacement

is known maximum time period for motion


Dwell

Constant Velocity

 

Parabolic (Constant-Acceleration - Constant-Deceleration) (PAR)

 

 

 

 

 

 

Simple Harmonic Motion (SHM)




Cycloidal




Polynomial 2-3




Polynomial 3-4-5




Polynomial 4-5-6-7




Modified Sinusoid

 

 

 

 

 

 

 

 

 

Modified Trapezoid