As mechanical stability of radiation therapy treatment devices has gone beyond sub-millimeter levels, there is a rising demand for simple yet highly accurate measurement techniques to support the routine quality control of these devices. A combination of using high-resolution radiosensitive film and computer-aided analysis could provide an answer. One generally known technique is the acquisition of star shot films to determine the mechanical stability of rotations of gantries and the therapeutic beam. With computer-aided analysis, mechanical performance can be quantified as a radiation isocenter radius size. In this work, computer-aided analysis of star shot film is further refined by applying an analytical solution for the smallest intersecting circle problem, in contrast to the gradient optimization approaches used until today. An algorithm is presented and subjected to a performance test using two different types of radiosensitive film, the Kodak EDR2 radiographic film and the ISP EBT2 radiochromic film. Artificial star shots with a priori known radiation isocenter size are used to determine the systematic errors introduced by the digitization of the film and the computer analysis. The estimated uncertainty on the isocenter size measurement with the presented technique was 0.04 mm (2σ) and 0.06 mm (2σ) for radiographic and radiochromic films, respectively. As an application of the technique, a study was conducted to compare the mechanical stability of O-ring gantry systems with C-arm-based gantries. In total ten systems of five different institutions were included in this study and star shots were acquired for gantry, collimator, ring, couch rotations and gantry wobble. It was not possible to draw general conclusions about differences in mechanical performance between O-ring and C-arm gantry systems, mainly due to differences in the beam-MLC alignment procedure accuracy. Nevertheless, the best performing O-ring system in this study, a BrainLab/MHI Vero system, and the best performing C-arm system, a Varian Truebeam system, showed comparable mechanical performance: gantry isocenter radius of 0.12 and 0.09 mm, respectively, ring/couch rotation of below 0.10 mm for both systems and a wobble of 0.06 and 0.18 mm, respectively. The methodology described in this work can be used to monitor mechanical performance constancy of high-accuracy treatment devices, with means available in a clinical radiation therapy environment.