Motion-Law Equations

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Motion-Law Equations

Motion-law Equations

When there is an equation for each derivative of a motion-law, they can be evaluated exactly.

For example:

If the normalized input, x, is 0.5467321892, then it is possible to evaluate exactly the normalized values of Position,Velocity, Acceleration, and Jerk for any of the motion-laws.


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


Functions, Input Variable.


Dwell

; ; ;

Constant Velocity

; ; ;

Constant-Acceleration, Constant-Deceleration (CACD)







Simple Harmonic Motion (SHM)




Cycloidal




Polynomial 2-3




Polynomial 3-4-5




Polynomial 4-5-6-7




Modified Sinusoid










Modified Trapezoid