Tripody: An Overconstrained 3-SPR-like Parallel Robot for High-Reach Construction Tasks

Many ceiling construction tasks still rely on heavy serial manipulators that are difficult to deploy in cluttered interiors, motivating lightweight, field-ready alternatives that reach ceiling height while maintaining millimeter-level accuracy and the stiffness demanded by overhead tool loads. We introduce Tripody, a wheeled 3-DoF parallel robot for high-reach tasks that replaces the base spherical joints of a classical 3-SPR (3 legs; S: base spherical joint; P: actuated prismatic joint; R: end-effector revolute joint) morphology with universal joints, intentionally overconstraining the mechanism; small, distributed elastic deflections absorb the resulting incompatibilities, preserving predominantly translational motion. The 33kg system extends from 1.7m to 3.4m in height, supports a continuous 32kg payload, and offers a modular end-effector interface for ceiling operations. We detail the mechanical design - including custom linear actuators and a kinematic-compatibility analysis - and a control stack for accurate positioning that combines SE(3) state estimation, forward kinematics, and task-space control. In experiments, Tripody exhibits similar in-plane stiffness to a spherical-base variant but substantially higher torsional stiffness - an increase of 67% at 1.7m, 196% at 2.6m, and 454% at 3.4m - while maintaining negligible cross-axis coupling. Closed-loop positioning with a total station converges below 0.6mm across the entire workspace; pure model extrapolation achieves a 95th-percentile error of 2.7mm (max 3.6mm). Finally, we demonstrate task-level ceiling-drilling feasibility in an open-loop study by drilling a 15-hole pattern with 4.5mm maximum relative hole-position error after rigid alignment. These results support overconstrained, compliance-absorbing 3-SPR-like architectures as a practical path to lightweight, high- reach, millimeter-accurate construction robots.