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Mathematics of Motion Control Profiles
You can get there from here
What a jerk
I Wanna Go Fast
Making Your Point-to-Point
Table for 65,536 Please
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Summary
 

Table for 65,536 Please

The ultimate in point-to-point profile generation, or in fact for other types of profiles including continuous path generation such as is used in CNC (Computer Numerical Control) machine tools, is to construct a custom profile that compensates for the exact load and motor characteristics of the system. Such a profile would accelerate the motor, taking into account the available motor torque at each velocity point, the mechanical resonances at each velocity point, and the actuator or arm kinematics in the mechanism.

Since motor torque curves do not follow simple mathematical principles, and because the equations for kinematic compensation are complex, these calculations are generally calculated in advance, and stored in a table of motion 'vectors'. This table is generally set up as an array of position or time vectors, with a corresponding entry for velocity and acceleration at each point of the curve.

In this configuration the motion engine is merely providing a generic capability to download and execute a list of vectors, and the responsibility of the calculations falls to the user. Despite this extra work, if special conditions exist, such as when motors or mechanisms are highly non-linear, table-driven point-to-point profiles can provide a meaningful performance increase, and may be worth the effort.



 
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