Full Circle Robot Path: Two Arcs, Not One Closed Arc

A full circle cannot be represented as one three-point circular movement because the start and end positions would coincide, leaving the interpolator without a unique arc. Build the circle as two connected semicircular movements, each defined by three distinct points on the same plane. Use four quarter arcs instead if the motion system rejects semicircles or changes tool orientation at the junction.

How do the symptoms identify a path-definition problem?

Look at the programmed path before changing motion settings. The circular movement accepts a start point, an intermediate point, and an end point, so it can describe an arc when those points are distinct and non-collinear. Asking the same interface to represent a full revolution makes the start and end coincide; the point triplet then fails to select one unique sweep.

This is a geometry-definition limitation, not evidence of poor servo tuning. Typical results include an invalid-path indication, a missing segment, an arc taking the unintended direction, or a preview that stops short of a full circle. The exact response depends on how the motion software validates coincident points and selects arc direction.

Why can three points define an arc but not a full circle?

Three distinct, non-collinear points define a circle in a plane. When they are interpreted as ordered motion points, they also identify a start position, a direction through the intermediate position, and an end position. That ordered definition describes a finite arc between different endpoints.

A full revolution ends where it starts. Substituting the start position for the end position removes the distinct endpoint the circular interpolator uses to determine the commanded sweep. The same coordinates could mean no movement, one revolution, multiple revolutions, or either direction around the circle. The component therefore needs another input—such as a center, plane, direction, sweep, or explicit closed-path property—to remove the ambiguity. The stated three-point interface provides none of those additional commands.

Splitting the trajectory restores a distinct endpoint for every movement. The first semicircle travels from one side of the circle to the opposite side through a quarter point. The second returns through the other quarter point. Together they produce one closed revolution without presenting coincident start and end positions to either circular command.

How should the full circle be constructed?

1. Define the process geometry. Establish the circle center, working plane, radius, tool orientation, and intended travel direction. For milling or plasma cutting, also decide where approach, process start, and departure occur; those moves are separate from the circular geometry.
2. Create four points on the same circle. Place them at successive quarter positions around the intended direction. The first point is the circle start, the third is diametrically opposite, and the second and fourth guide the two halves.
3. Program the first circular movement. Use the start point, the first quarter point, and the opposite point as the three ordered inputs. These distinct, non-collinear points define the first semicircle.
4. Program the second circular movement. Use the opposite point, the second quarter point, and the original start point. Maintain the same direction around the circle.
5. Match pose data at the junction. The end pose of the first segment and start pose of the second must represent the same position and tool orientation. A position-only match does not prevent an orientation jump.
6. Keep process control separate. Start the spindle, cutting output, or other process command before entering the finished contour, and stop it only after leaving the cut when the application requires lead-in or lead-out motion.
7. Preview at reduced risk. Inspect both arcs in the path display, then dry-run above or away from the work before executing the cutting trajectory.

If a semicircle is rejected because of how the application handles a 180-degree sweep, divide the path into four quarter-circle movements. Each command then receives a start point, a distinct intermediate point between quarter positions, and a distinct end point. Do not insert arbitrary offsets to force validation; offsets change the radius and can leave a visible mismatch at closure.

What does the robot controller do with the segmented path?

The path generator sends two valid circular commands rather than one ambiguous command. The controller interpolates the first arc to the opposite point, transitions to the second command, and returns to the original position. Robot kinematics then convert the tool-center-point trajectory into joint targets for the axes.

The geometric join can be exact while the physical motion still slows or stops there. Whether the controller blends adjacent movements depends on its motion settings and on continuity of position, tangent direction, velocity, acceleration, tool orientation, and robot configuration. Adjust blending only after confirming that both arcs share the same circle and tangent. Motion smoothing cannot repair mismatched endpoints, unequal radii, or reversed point order.

A proposed close-path input would be convenient, but closure alone would not necessarily command circular interpolation. A generic close function may only connect the last point to the first with another segment. Use such a feature only when its documentation explicitly states that it preserves the intended circular geometry and full-revolution direction.

How is the result verified before cutting?

1. Inspect the preview. Confirm that the two arcs form one circle, use the intended plane, and travel in the same direction.
2. Check the join. Compare the first arc's endpoint with the second arc's start point, including tool orientation. Check the final point against the original start pose.
3. Check tangency. The path direction entering and leaving the shared opposite point must be continuous. A corner or cusp indicates incorrect point order or inconsistent geometry.
4. Review the complete robot motion. Simulate or dry-run the path while watching joint motion, reach, configuration changes, and clearance. A valid Cartesian circle does not guarantee a feasible joint trajectory.
5. Run slowly without the process active. Observe the tool-center point at both segment boundaries. Investigate any pause, reversal, wrist excursion, or departure from the plane before enabling the mill or plasma process.
6. Measure the produced feature. Check diameter, roundness, closure, and any witness mark at the segment junction. Correct geometry or calibration errors before changing controller dynamics.

Which pitfalls recur with segmented circles?

Collinear point triplets do not define a circle, and nearly collinear points make the computed center sensitive to coordinate error. Reusing the start point as the endpoint of one command recreates the original ambiguity. Reversing the intermediate points can also command opposite sweep directions, producing an overlap, reversal, or unexpected long arc.

Duplicated coordinates with different orientations are another common failure. The tool reaches the correct location but rotates at the join because the two poses do not agree. Likewise, independently constructed arcs may have slightly different centers or radii; the preview can appear closed while the cut contains a step or tangent discontinuity.

Do not compensate for these faults with speed, blend, or servo adjustments. First validate point coordinates, plane, order, radius, orientation, and path continuity. Then evaluate interpolation settings and process-specific lead-in or lead-out behavior.

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