cs.ROFeb 16, 2026
SaveAnalysis of a Cuspidal 6R Robot
Organizations: OTH Regensburg, 93053 Regensburg, Germany
Abstract
We present a theoretical and numerical analysis of the kinematics for the "Transpressor", a cuspidal 6R robot. It admits up to 16 inverse kinematics solutions which are described geometrically. For special target poses, we provide the solutions analytically and present a simple numerical solver for the general case. Moreover, an analytical estimate of the Jacobian determinant on a path between two solutions proves cuspidality for a class of robots similar to the transpressor.
Figures & tables
Figure 1: a The KUKA Transpressor, b our simplified version in home position (the red indication of axis is shifted along for visibility), and c the table of DH-parameters
Figure 2: Some IKS for a pose with vertical -axis with a elbow up/down configurations, wrist outwards, and b left/right configurations, elbow down
Figure 3: A pose with IKS, in each elbow configuration. Considering both shoulder configurations yields a total of IKS. For the solid blue configuration, we indicated the direction of the axes with red lines. Note that axis is tangential to the circle.
Figure 4: Two configurations to reach a pose on the -axis: left configuration with elbow up and no wrist flip (blue), and right configuration with elbow up and wrist flipped (green)