Arc-to-Arc Transitions

In arc-to-arc transition mode, the transitions are processed as.

  1. The arc with the larger radius is shortened by an arc length equal to the corner distance.
  2. Using this point, a transition move is calculated such that it is tangent to both arcs.
  3. The arc with the smaller radius is shortened to the point where it is tangent with the transition move.

The transition move that connects the two original arcs derives its velocity from the velocity transition parameter and the acceleration and deceleration values are derived from the next move.

These are the special cases for Arc-to-Arc transitions:

Intersection Transition

This occurs when the arcs intersect at two locations and the corner distance is equal to the arc length between the two intersections on the larger arc.

  • The transition move is zero distance.
  • If the buffer mode is Buffered, the path velocity goes to zero.
  • All other buffer modes may cause a large acceleration and jerk.

Motion Path -
Line-to-Arc / Arc-to-Line

Key

Motion Velocity Profile

Blue: Incoming and outgoing circular motion.

Black: Trimmed path.

  1. Intersection of the two arcs.

Line Segment Transition

  • For certain values of corner distance, the transition arc has an infinite radius.
    • A line segment is used instead.

Motion Path -
Line-to-Arc / Arc-to-Line

Key

Motion Velocity Profile

Blue: Incoming and outgoing circular motion.

Red: Line Segment.

  1. Start / endpoint of transition move.

Same Circle: Opposite Direction Transition

The arcs are shorted by an arc length equal to the corner distance.

  • A zero distance transition is inserted if both arcs lie on the same circle and are in the opposite direction.
  • If the buffer mode is Buffered, the path velocity goes to zero.
  • All other buffer modes may cause a large acceleration and jerk.

Motion Path -
Line-to-Arc / Arc-to-Line

Key

Motion Velocity Profile

Blue: Incoming and outgoing circular motion.

  1. Original start / endpoint of arc move.
  2. Start / endpoint of arc move.

n-Degree: Arcs in Opposite Direction

Motion Path -
Line-to-Arc / Arc-to-Line

Key

Motion Velocity Profile

Blue: Incoming and outgoing circular motion.

Black: Trimmed path.

Red: Transition arc.

  1. Start / endpoint of arc move.

Same Circle: Same Direction Transition

A transition arc with a length of twice the corner distance is added if both arcs lie on the same circle and are in the same direction.

  • This does not affect the path but does affect blending.

Motion Path -
Line-to-Arc / Arc-to-Line

Key

Motion Velocity Profile

Blue: Incoming and outgoing circular motion.

Red: Transition arc.

  1. Start / endpoint of arc move.
  2. Original start / end point.

n-Degree: Arcs in Same Direction

Motion Path -
Line-to-Arc / Arc-to-Line

Key

Motion Velocity Profile

Blue: Incoming and outgoing circular motion.

Black: Trimmed path.

Red: Transition arc.

  1. Start / endpoint of arc move.
  2. Corner distance.

Tangent Transition: Opposite Direction

A portion of the arc with the larger radius is replaced by an arc whose length is equal to the corner distance.

  • If the arcs have the same radius, the incoming arc is treated as having a larger radius.
  • This does not affect the path but does affect blending.

Motion Path -
Line-to-Arc / Arc-to-Line

Key

Motion Velocity Profile

Blue: Incoming and outgoing circular motion.

Red: Transition arc.

  1. Original start / end point of moves.
  2. Start / endpoint of arc move.

Zero-distance Transition

A zero-distance transition move is inserted when the corner distance is zero.

  • This only affects blending.
  • If the buffer mode is Buffered, the path velocity goes to zero.
  • All other buffer modes may cause a large acceleration and jerk.

Motion Path -
Line-to-Arc / Arc-to-Line

Key

Motion Velocity Profile

Blue: Incoming and outgoing circular motion.

  1. Original start / endpoint of arc move.

User unit/sec