A Greedy Algorithm for Feed-rate Planning of CNC Machines along Curved Tool Paths with Confined Jerk for Each Axis
نویسندگان
چکیده
The problem of optimal feed-rate planning along a curved tool path for 3-axis CNC machines with a jerk limit for each axis is addressed. We prove that the optimal feed-rate planning must use “Bang-Bang” control, that is, at least one of the axes reaches its jerk bound throughout the motion. As a consequence, the optimal parametric velocity can be expressed as a piecewise analytic function of the curve parameter u. We also give the explicit formula for the velocity function by solving a second order differential equation. Under a “greedy rule”, an algorithm for optimal jerk confined feed-rate planning is presented, together with an example.
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