Position control method in which a cartesian point is transformed through two cartesian coordinate systems

Claim 1

A position control method for performing pulse distribution processing based on position data coordinates (x, y, z) in a three-dimensional program coordinate system, and controlling the position of a movable element on the basis of data obtained by said pulse distribution processing, comprising: a first step of obtaining, in the program coordinate system, a central axis vector (i o , j o , k o ) of a first rotational axis, coordinates (x co , y co , z co ) of a rotational center point on said first rotational axis, and an angle of rotation θ, and defining a central axis vector (i 1 , j 1 , k 1 ) of a second rotational axis in a new three-dimensional coordinate system determined by rotation of the program coordinate system through θ, coordinates (x c1 , y c1 , z c1 ) of a rotational center point on said second rotational axis, and an angle of rotation φ; a second step of calculating a transformation matrix [M 1 ] using the central axis vector (i o , j o , k o ) of the first rotational axis and θ, wherein coordinates (x 1 , y 1 , z 1 ) in the new three-dimensional coordinate system are obtained, when coordinates (x, y, z) in the program coordinate system are rotated by θ about the first rotational axis, in accordance with the following equation: ##EQU8## and calculating a transformation matrix [M 2 ] using the central axis vector (i 1 , j 1 , k 1 ) and φ, wherein coordinates (x 2 , y 2 , z 2 ) are obtained, when the new three-dimensional coordinate system is rotated by φ about the second rotational axis, in accordance with the following equation: ##EQU9## a third step of transforming the position data coordinates (x, y, z) in accordance with the following equation: ##EQU10## and a fourth step of moving a movable element along a path based on the transformed position data (x', y', z').