## 1 Introduction  
The bodyweight wall squat is a popular physical exercise frequently included in the early stage of lower limb rehabilitation interventions [1]. It can also be used to promote exercise-induced hypoalgesia [2], increase the thickness of deep abdominal muscles [3], improve posture [4] and lumbar stability [3], and reduce resting blood pressure in home-based training [5]. The support provided by the wall during the wall squat considerably reduces the balance and stability demands, compared to the free squat. For this reason, the wall squat constitutes a functional lower limb exercise that can be included in the early stage of rehabilitation interventions, as soon as the patient can tolerate weight bearing [1]. In the early subacute phase of lower limb rehabilitation, and particularly during the transition from partial to full weight-bearing, squat exercises should necessarily be performed with no external resistance and with the aid of external stabilization supports. A progression involving mini-squat with upper extremity assistance and bodyweight wall squat can be safely employed in this phase [1]. In the starting position, the exercise stands with the back flat against the wall (any flat vertical surface with negligible friction), knees fully extended, arms straight at the sides of the body, feet flat on the floor about shoulder-width apart. The horizontal distance \(d\) of the ankle from the hip (which nearly coincides with the heel-to-wall distance) determines the hip and ankle angle in the starting position and constitutes the main variant of the exercise. From the starting position, the exerciser slowly flexes the knees and slides down the wall until the desired degree of knee flexion is reached. In the isometric wall-squat exercise, this position is held for a selected time before the subject returns back to the starting position. In the dynamic wall-squat exercise, the eccentric (descending) phase of the exercise is followed in a continuous motion by the concentric (ascending) phase. During the entire exercise, the subject should maintain a neutral spine position, the back vertical against the wall, a proper knee alignment (to avoid knee varus/valgus and internal/external rotation), and feet flat on the floor. From a kinematic perspective, the wall-squat exercise has only one degree of freedom: given the distance \(d\) and the exerciser's anthropometry, the configuration of the body in each phase of the exercise is completely determined by only one parameter, e.g., the hip height from the ground or the knee angle \(\theta_{\text{knee}}\). Despite the popularity and importance of the _bodyweight_ wall squat, a quantitative biomechanical analysis of this exercise is lacking. In 1999, [PERSON] [6] published an electromyographic (EMG) study for the dynamic bodyweight wall squat performed from full knee extension to 60\({}^{\circ}\) of knee flexion, in two different conditions of foot position (foot in line with the hip and foot 50 cm forward) and posterior support location (at hip level and scapular level). In that study, the mean EMG activity of gluteus maximus, semitendinosus, vastus lateralis, and medial gastrocnemius was recorded during three consecutive repetitions. Notably, to date, no study has provided information related to the joint torques, joint reaction forces, and forces acting on specific joint structures during the _bodyweight_ wall-squat exercise. Knowledge and control of the joint torques and forces acting during the execution of a physical exercise is of paramount importance for safe and effective implementation of the exercise in rehabilitation and training programs. The main aim of this study was to provide an in-depth quantitative biomechanical analysis of the bodyweight wall-squat exercise, in static condition, accounting for all relevant exercise positions and variants.