In human movement modeling, the problem of multi-link kinematics estimation by means of inertial measurement units has been investigated by several authors through efficient sensor fusion algorithms. In this perspective a single inertial measurement unit per link is required. This set-up is not cost-effective compared with a solution in which a single-axis accelerometer per link is used. In this paper, a novel fast technique is presented for the estimation of the sway angle in a multi-link chain by using a single-axis accelerometer per segment and by setting the boundary conditions through an ad hoc algorithm. The technique, based on the windowing of the accelerometer output, was firstly tested on a mechanical arm equipped with a single-axis accelerometer and a reference encoder. The technique is then tested on a subject performing a squat task for the knee flexion-extension angle evaluation by using two single-axis accelerometers placed on the thigh and shank segments, respectively. A stereo-photogrammetric system was used for validation. RMSEs (mean ± std) are 0.40 ± 0.02° (mean peak-to-peak range of 147.2 ± 4.9°) for the mechanical inverted pendulum and 1.01 ± 0.11° (mean peak-to-peak range of 59.29 ± 2.02°) for the knee flexion-extension angle. Results obtained in terms of RMSE were successfully compared with an Extended Kalman Filter applied to an inertial measurement unit. These results suggest the usability of the proposed algorithm in several fields, from automatic control to biomechanics, and open new opportunities to increase the accuracy of the existing tools for orientation evaluation.