A delta robot inverts the usual robot-arm layout: three identical arms hang from a fixed base and all drive a single moving platform in parallel, so only three motors are needed for 3-DOF translation. This 2D companion draws the exact same per-arm inverse-kinematics solve as the 3D version, split into two views instead of one 3D scene: a top-down base view showing where the target sits relative to all three shoulders, and — for each arm — its own "unfolded" radial/vertical plane, the 2D cross-section the equation actually solves in.
Each arm's motor swings a rigid bicep of length rf in the vertical plane through its own shoulder. For arm i at base angle αi (120° apart), the target is projected into that arm's radial/vertical plane, and the elbow angle θi is solved from the constraint that the forearm (length re) must exactly reach the platform attachment point:
shoulder = Fr·radial̂ᵢ
attach = target + Er·radial̂ᵢ (Er = platform attach radius)
r = (attach − shoulder) · radial̂ᵢ (in-plane reach)
t = (attach − shoulder) · tangent̂ᵢ (out-of-plane offset, absorbed by the forearm)
h = depth below base
r·cosθᵢ − h·sinθᵢ = (r²+h²+rf² − (re²−t²)) / (2·rf) ← solve for θᵢ
This is a circle-circle intersection in the arm's own plane — exactly what the right-hand panel draws for each arm: the bicep's reach circle (radius rf around the shoulder) meeting the forearm's reach circle (radius √(re²−t²) around the attach point). Two candidate angles solve it; the solver keeps the one with the more "outward" elbow, the non-self-colliding configuration real delta robots run in.
- X / Z / Depth sliders — move the target point directly; all three θᵢ update instantly from the equation above.
- Run Demo Cycle — plays the classic arch motion: descend at the pick zone, retract, translate, descend at the place zone, retract, and repeat.
- Reachable envelope — the dashed circle in the top view is the horizontal reach limit; a red angle box means that arm's forearm cannot reach the current target at all (a real delta robot would stall here).