Speech signal analysis is a powerful tool that facilitates the monitoring and tracking of symptom deterioration caused by neurodegenerative disorders, typically achieved using either sustained vowels, diadochokinetic ex-ercises or running speech. This study expands our previous work on the study of the movement produced by the jaw-tongue biomechanical system. The aim is to further investigate the effects of neuromotor activity during muscular exertion that translates formant acoustics into speech articulatory movements affected by hypokinetic dysarthria in Parkinson’s Disease (PD). The objective of this study is to estimate the parameters of an inverse acoustic-to-kinematic projection model that takes as an input the variations of the first and second formants and estimates as output the spatial variation of the jaw-tongue biomechanical system. The spatial variations have been extracted from 3D accelerometry (3DAcc). These serve as ground truth for comparison with the estimated activity projected from speech kinematics, as a measure of fitness of the inverse model. The estimation method is a two step process: first initial weight values are produced using multiple regression between each of the formant dynamic signals (acoustical analysis) and the estimated spatial variations (accelerometry). The second step uses a weight refinement method based on gradient-descent. Additionally, a time-realignment study has been carried out on the acoustic-to-kinematic projection model, based on the estimation of relative time displacements as to maximize the cross-correlation between signals. The study is complemented with an estimation of the model weights on a dataset from PD participants and Healthy Controls (HC). This methodology opens up new ways to investigate the underlying physiological voice production mechanism which may offer new insights into PD symptoms.