Circular Interpolation
A circular interpolation command interpolates the cyclic position commands of two or three axes to move in an arc formed by part of a circle, an entire circle, or multiple loops around a circle.
A two-dimensional circular interpolation can be defined in the following ways.
Center and Length
Center and End
Through and End
Length and End
Radius and End
Through and End 3D
Center and Length
In this circular interpolation type, the center position and the arc length of the circular trajectory are specified using the CenterAndLengthCircularIntplCommand class.
The center position may be specified as an absolute position or a relative position.
The arc length is specified in units of degrees. The arc length may be greater than 360 degrees, in which case the circular trajectory will rotate more than one full circle.
The following diagram shows the parameters if the center position is specified as an absolute position.
In this diagram, (S1, S2) is the starting position, (C1, C2) is the center position, and d is the arc length in degrees. Whether the direction of rotation is clockwise or counterclockwise must also be specified.
The following diagram shows the parameters if the center position is specified as a relative position.
In this diagram, (S1, S2) is the starting position, c1 and c2 are the relative distances to the center position, and d is the arc length in degrees. Whether the direction of rotation is clockwise or counterclockwise must also be specified.
Center and End
In this circular interpolation type, the center position and the end position of the circular trajectory are specified using the CenterAndEndCircularIntplCommand class.
The center and end positions may be specified as absolute positions or relative positions.
The end position may be the same position as the starting position, in which case the circular trajectory will be a 360 degree arc. The arc may not be greater than 360 degrees.
The following diagram shows the parameters if the center and end positions are specified as absolute positions.
In this diagram, (S1, S2) is the starting position, (C1, C2) is the center position, and (E1, E2) is the end position. Whether the direction of rotation is clockwise or counterclockwise must also be specified.
The following diagram shows the parameters if the center and end positions are specified as relative positions.
In this diagram, (S1, S2) is the starting position, c1 and c2 are the relative distances to the center position, and e1 and e2 are the relative distances to the end position. Whether the direction of rotation is clockwise or counterclockwise must also be specified.
Depending on the specified center position, the end position may not lie on the perimeter of the circle. If this occurs, the center position is adjusted to the closest position that would cause the end position to lie on the perimeter of the circle. The following diagram illustrates this adjustment of the center position.
In this diagram, (S1, S2) is the starting position, (E1, E2) is the end position, (C1, C2) is the specified center position, and (C1’, C2’) is the center position after it is adjusted so that the end position lies on the perimeter of the circle.
Through and End
In this circular interpolation type, the end position and an intermediate position that the circular trajectory passes through are specified using the ThroughAndEndCircularIntplCommand class.
The end and through positions may be specified as absolute positions or relative positions.
The following diagram shows the parameters if the end and through positions are specified as absolute positions.
In this diagram, (S1, S2) is the starting position, (E1, E2) is the end position, and (I1, I2) is an intermediate position that the circular trajectory passes through.
The following diagram shows the parameters if the end and through positions are specified as relative positions.
In this diagram, (S1, S2) is the starting position, e1 and e2 are the relative distances to the end position, and i1 and i2 are the relative distances to an intermediate position that the circular trajectory passes through.
Length and End
In this circular interpolation type, the end position and the arc length of the circular trajectory are specified using the LengthAndEndCircularIntplCommand class.
The end position may be specified as an absolute position or a relative position.
The arc length is specified in units of degrees. The arc length must be less than 360 degrees.
The following diagram shows the parameters if the end position is specified as an absolute position.
In this diagram, (S1, S2) is the starting position, (E1, E2) is the end position, and d is the arc length in degrees. Whether the direction of rotation is clockwise or counterclockwise must also be specified.
The following diagram shows the parameters if the end position is specified as a relative position.
In this diagram, (S1, S2) is the starting position, e1 and e2 are the relative distances to the end position, and d is the arc length in degrees. Whether the direction of rotation is clockwise or counterclockwise must also be specified.
Radius and End
In this circular interpolation type, the end position and the radius of the circular trajectory are specified using the RadiusAndEndCircularIntplCommand class.
The end position may be specified as an absolute position or a relative position.
The following diagram shows the parameters if the end position is specified as an absolute position.
In this diagram, (S1, S2) is the starting position, (E1, E2) is the end position, and r is the radius. A positive radius generates an arc between 0 and 180 degrees, and a negative radius generates an arc between 180 and 360 degrees. Whether the direction of rotation is clockwise or counterclockwise must also be specified.
The following diagram shows the parameters if the end position is specified as a relative position.
In this diagram, (S1, S2) is the starting position, e1 and e2 are the relative distances to the end position, and r is the radius. A positive radius generates an arc between 0 and 180 degrees, and a negative radius generates an arc between 180 and 360 degrees. Whether the direction of rotation is clockwise or counterclockwise must also be specified.
3D Through and End
In this circular interpolation type, the end position and an intermediate position that the circular trajectory passes through are specified in three-dimensional space using the ThroughAndEnd3DCircularIntplCommand class.
The end and through positions may be specified as absolute positions or relative positions.
The following diagram shows the parameters if the end and through positions are specified as absolute positions.
In this diagram, (S1, S2, S3) is the starting position, (E1, E2, E3) is the end position, and (I1, I2, I3) is an intermediate position that the circular trajectory passes through.