SCARA Robot Arm Workspace Envelope Calculator

The SCARA workspace envelope is the planar spatial region that the robot tool center point (TCP) can physically access.

Because links rotate about parallel vertical axes, the reachable horizontal space forms a circular annulus or sector.

Maximum reach is achieved when both links are fully outstretched in line (theta2 = 0 deg).

The inner circular dead zone occurs when link 2 folds entirely back against link 1 (theta2 = 180 deg).

The optimal dexterity radius occurs when the two links meet at 90 degrees, maximizing the determinant of the kinematic Jacobian.

Maximum reach gives the outermost cylindrical operating radius.

Minimum inner radius defines the central dead zone where the arm cannot physically fold.

The dexterity sweet spot indicates the operating radius with greatest speed and trajectory accuracy.

• Link length ratio: Equal link lengths (L1 = L2) collapse the inner dead zone to zero radius at the center.
• Joint travel stops: Physical hard stops limit rotation, converting full annuli into toroidal sectors.
• Cable harnesses: Cabling bundles behind the elbow often reduce joint 2 rotation to under 300 degrees.

• Sizing automated workcells, assembly tables, and conveyor feeder placements.
• Evaluating whether an existing robot arm can reach all pick and drop bins without link collisions.

• Assumes planar 2D horizontal motion without vertical Z-axis quill stroke or tool flange offsets.
• Does not account for physical link collision geometry or rear cable dress clearances.