This research investigates the robotic assembly of timber structures connected by wood–wood connections. As the digitization of the timber construction sector progresses, digital tools, such as industrial robotic arms and Computer Numerical Control machines, are becoming increasingly accessible. The new-found ease with which wood can be processed stimulates a renewed interest in traditional joinery, where pieces are simply interlocked instead of being connected by additional metallic parts. Previous research established a computational workflow for the robotic assembly of timber plate structures connected by wood–wood connections. This paper focuses on determining the physical conditions that allow inserting through-tenon joints with a robot. The main challenge lies in minimizing the clearance between the tenon and the mortise in order to keep the connections as tight as possible. An experimental protocol has, therefore, been developed to quantitatively assess the performance of the insertion according to different geometric parameters. Robotic insertion tests have been carried out on over 50 samples of 39 mm Laminated Veneer Lumber. Results showed the interest of tapering the joint with a 5 degrees angle, in addition to introducing an offset of 0.05 mm, to minimize friction forces during the insertion. This configuration was confirmed by successfully assembling a 2,50 m long box girder with the same parameters.