Cam Motion Synthesis Using Spline Functions

Abstract

The application of spline functions to the general synthesis of cam motion programs is presented. The approach provides a single, systematic, easily automated method of accommodating discrete constraints on follower displacements, velocities, and accelerations, even when the set of constraints becomes large. Yet, it is as easily applied in simple cases as are the more traditional methods of syntheses. It also allows the designer to refine the motion program by locally influencing characteristics of the motion while still satisfying the discrete constraints. A series of examples is presented to illustrate application of the method and to compare it to the more traditional techniques.

Optimal Splines for Rigid Motion Systems: A Convex Programming Framework

“…Internal knot t i is called active if the kth-order derivative of s(t) is discontinuous at t i , while at an inactive internal knot, the kth-order derivative of s(t) is continuous. The definition (1)- (2) implies that the fundamental law of cam design dictates the use of at least cubic (k = 3)…”

“…Figure 1 shows a cubic spline θ(τ) and its first three derivatives as a function of (dimensionless, see further) time τ, where 0 ≤ τ ≤ 2π. The spline consists of 3rd-degree polynomial segments and, as allowed by (2), features discontinuous jumps of the 3rd-order derivative at all spline knots, except for the knots at τ = 1.0 and τ = 5.0. The former knots are active knots, as opposed to the redundant, inactive knots τ = 1.0 and τ = 5.0.…”

“…Our particular contributions are the following. 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].…”

“…Polynomial splines entered the area of cam design in the early 1980s (see the references provided in [1]) and were quickly recognized as being more flexible than combining and modifying standard analytical curves, especially for complex motion tasks with a large array of constraints [2]. Splines have currently replaced polynomials as the mathematical descriptors of valve motion about anywhere in automotive industry [3].…”

Homojen Dolgulu Sıkıştırma İle Ateşlemeli Bir Benzin Motoru İçin Kam Tasarımı Ve İmalatı

“…Kam tasarımında yaygın olarak kullanılan metotlardan bir diğeri fourier serileridir. Araştırmacılar fourier serilerini kullanarak süperpozisyon prensibine dayanan metot ile kam tasarımlarını gerçekleştirmişlerdir [6][7][8][9][10].…”