This paper covers the design of a new multi-point kinematic coupling specially developed for a high precision multi-telescopic arm measurement system for the volumetric verification of machine tools with linear and/or rotary axes. The multipoint kinematic coupling allows the simultaneous operation of the three telescopic arms that are registered at the same time to a sphere fixed on the machine tool spindle nose. Every coupling provides an accurate multi-point contact to the sphere, avoiding collisions and interferences with the other two multi-point kinematic couplings, and generating repulsion forces among them to ensure the coupling’s fingers interlacing along the machine tool x/y/z travels in the verification process. Simulation presents minimal deformation of the kinematic coupling under load, assuring the precision of the sphere-to-sphere distance measurement. Experimental results are provided to show that the multi-point kinematic coupling developed has repeatability values below ±1.2 µm in the application.