Parallel Mechanisms: Delta Robots

A delta robot holds its tool platform with three arms instead of one. All three motors sit on the fixed base, so the moving parts are light and fast. Delta robots pick and place items on packaging lines hundreds of times per minute.

Platform x Platform y Platform z Show the workspace Move in a pick-and-place loop

Drag the 3D view to look from another angle.

Inverse kinematics is easy here

For a serial arm, forward kinematics is easy and inverse kinematics is hard. For a delta robot it is the other way around. Given a platform position $\mathbf{p}$, each arm $i$ has a closed-form angle: the upper arm of length $L_u$ must reach a point whose distance from the platform joint equals the forearm length $L_f$:

$$\big\lVert \mathbf{e}_i(\mathbf{p}) - \mathbf{b}_i - L_u\,\mathbf{u}(\theta_i) \big\rVert = L_f \qquad i = 1, 2, 3$$

Each equation gives one $\theta_i$. The parallelogram forearms keep the platform level at all times, so a delta robot moves in x, y, and z without tilting.

What to notice

The gray cloud is every point the platform can reach. It is shaped like a lens hanging below the base. Push the platform toward the edge and one arm straightens toward its limit, and the readout reports when a position is out of reach. Because the motors do not ride on the arms, delta robots can accelerate many times faster than gravity.