Circular Interpolation

SYNOPSIS OF PROJECT

CIRCULAR INTERPOLATION

SUBMITTED BY

SWATHI RAO B

INTRODUCTION:

Interpolation is a method of constructing new data points within the range of a discrete set of known data points & it is a specific case of curve fitting, in which the function must go exactly through the data points. Interpolation is available with motion controllers which are very expensive. Interpolation to be available with non motion controllers will be a cost effective solution.

Circular interpolation

The generation of an apparently circular motion through the coordinated movements of two axes. The actual path is a series of straight line approximations generated by software algorithms.

EXPLANATION:

The main aim of the project is to control the movement of the axes to create a circular motion. The design and implementation are explained below in brief

1. Design:

To understand the principles of programming various circular motions, basic geometry of a circle is considered.

If X axis is commanded to perform cosine function & y axis to perform sine function then resultant is a circle.

• Data required to generate a circle:

1. Radius

2. velocity

3. centre point

4. start point & endpoint(to generate arc)

The objective is to identify values of (X, Y) coordinates on the circumference.

Circumference of the circle is sampled into ‘N’ number of points. Coordinates of each point are derived from circular equation.

[pic]

To get (X, Y) coordinate value the following formulae is used

[pic]

Where, (h, k) is the centre of the circle with ‘r’ radius & theta is the angle at centre to the points on the circumference of the circle.

2. Implementation:

Consider two points A(X1, Y1) & B(X2, Y2) on the circumference. To travel from A to B, linear coordinated motion is...