Computer aided design of cam motion programs

Optimal Splines for Rigid Motion Systems: A Convex Programming Framework

“…2 If the knot sequence is increasing, but not strictly increasing (that is, coincident knots are present), the continuity condition (2) has to be relaxed. (i) Simplifying spline optimization by providing a set of fixed candidate knots and only optimizing spline coefficients is not a new idea [4,[7][8][9][10][11]13]. Contrary to our approach, however, the number of knots was previously always kept limited (generally 5-20, as opposed to a few hundreds or thousands here), even if the effect of increasing the number of knots was investigated [7,9,11].…”

“…The important role of convexity as the key criterion making an optimization problem 'easy' or 'difficult' seems to be little known in the area of spline optimization for motion systems. While Sections 3 and 4 focus on linear programs, a subclass of convex programs, Section 5 makes the extension to convex programs by reviewing the known optimization methods [4,[7][8][9][10][11][12][13] thereby showing that some of these methods can be extended or simplified based on insights from convex optimization theory.…”

“…That is, instead of computing θ (q) (τ i ) from Eq. (9), it is computed by the following recursive relation, which is only valid for the equidistant knot spacing defined by (8), and follows from elementary calculus (i = 1, . .…”

“…A more automated approach results if the spline knots are determined based on numerical optimization [4,[7][8][9][10][11][12][13] for it provides a mathematical framework in which many design objectives and constraints can be included. Numerical optimization looks very attractive, since it seems to suffice to push a button to automatically obtain a solution that optimizes the design objective while complying with all design constraints.…”

Optimising cam motion using piecewise polynomials

“…Wang and Yang [5] used a quadratic programming (QP) algorithm to optimise the shape of the motion profile created using PP such that the jerk level is reduced to a minimum. The optimisation is carried out using any unspecified breakpoint boundary conditions as variables.…”