In clinical movement biomechanics, kinematic measurements are collected to characterise the motion of articulating joints and investigate how different factors influence movement patterns. Representative time-series signals are calculated to encapsulate (complex and multidimensional) kinematic datasets succinctly. Exacerbated by numerous difficulties to consistently define joint coordinate frames, the influence of local frame orientation and position on the characteristics of the resultant kinematic signals has been previously proven to be a major limitation. Consequently, for consistent interpretation of joint motion (especially direct comparison) to be possible, differences in local frame position and orientation must first be addressed. Here, building on previous work that introduced a frame orientation optimisation method and demonstrated its potential to induce convergence towards a consistent kinematic signal, we present the REference FRame Alignment MEthod (REFRAME) that addresses both rotational and translational kinematics, is validated here for a healthy tibiofemoral joint, and allows flexible selection of optimisation criteria to fittingly address specific research questions. While not claiming to improve the accuracy of joint kinematics or reference frame axes, REFRAME does enable a representation of knee kinematic signals that accounts for differences in local frames (regardless of how these differences were introduced, e.g. anatomical heterogeneity, use of different data capture modalities or joint axis approaches, intra- and inter-rater reliability, etc.), as evidenced by peak root-mean-square errors of 0.24° ± 0.17° and 0.03 mm ± 0.01 mm after its implementation. By using a self-contained optimisation approach to systematically re-align the position and orientation of reference frames, REFRAME allows researchers to better assess whether two kinematic signals represent fundamentally similar or different underlying knee motion. The openly available implementation of REFRAME could therefore allow the consistent interpretation and comparison of knee kinematic signals across trials, subjects, examiners, or even research institutes.