In CNC/robotic machining or motion control, straight-line operations do not have to align with coordinate axes; linear motions can include diagonal cuts as long as the path is not curved.

Introduction / Context:
In computer numerical control (CNC) and robotic motion planning, a “straight-line” operation refers to a linear interpolation between two points in space. Controllers execute linear moves (e.g., G01 in CNC) along any vector defined by start and end coordinates. This includes directions that are not aligned with principal axes, such as diagonal paths in the XY plane or along 3D tool vectors.

Given Data / Assumptions:

• The coordinate system is defined, but paths can be arbitrary vectors.
• Linear motion means zero curvature along the path segment.
• The workpiece may require angled or diagonal edges.

Concept / Approach:
Linear interpolation calculates intermediate points along the line between two endpoints using constant or controlled feed. Nothing in the definition requires alignment with axes. Axis-parallel moves are common, but diagonal moves are equally valid and often necessary. Limits arise from machine kinematics and feed/speed constraints, not from a geometric prohibition on diagonals.

Step-by-Step Solution:
Define linear motion: path with constant direction vector and zero curvature.Map to controller capability: linear interpolation between arbitrary points.Evaluate options: axis-parallel is a subset; diagonal qualifies as long as the path is straight.Select the statement allowing diagonal, non-curved cuts.

Verification / Alternative check:
CNC programs routinely include moves like G01 X50 Y50 from X0 Y0, which is a diagonal straight line. CAM software outputs such segments for chamfers and angled features.

Why Other Options Are Wrong:
Limited to two per workpiece: arbitrary and false.Must be parallel to an axis: incorrect; linear motion can be any direction.All of the above: false because previous statements are incorrect.None of the above: wrong since option C is correct.

Common Pitfalls:
Confusing linear interpolation with step-over raster strategies; assuming tool orientation constraints prohibit diagonals when, in fact, they limit orientation, not linearity.

Final Answer:
Can include diagonal cuts if they are not curved