Modeling and solving discrete Archimedean spiral motion based on forward difference algorithm

The kinematic behavior of Archimedean spiral curves composed of discrete points has a wide range of applications. In this paper, a numerical modeling method is proposed based on the forward difference algorithm, which is able to accurately describe the position and velocity of discrete points in spiral motion. For the two cases that the spiral curve stops moving and the direction of motion is changed, we construct the geometric constraints and functions, and verify the accuracy and applicability of the model through the arithmetic examples, which provides the basis for further research on the spiral motion under complex geometric constraints.