## 2 Materials and Methods
### Foot Angles Definition  
Our model allowed us to measure any movement pertaining to the foot bones. Properly identifying the reference axes is essential to identify the angles deserving clinical attention. We concentrated our attention on the following joint angles:  
* The forefoot dorsiflexion/plantarflexion angle and forefoot supination/pronation angle. A mediolateral axis, fixed to the distal tibia and passing through the centre of curvature of the tibial trochlea, was adopted as the dorsi/plantarflexion axis (see revolute joint A in Figure 2). A bar (labelled L in Figure 2), representing the longitudinal axis of the foot, was connected to revolute joint A, while the other extremity of the bar was connected to the forefoot. Since the bar could only move in a plane perpendicular to the dorsi/plantarflexion axis, the connection with the forefoot was defined as follows: a transverse bar labelled F was connected to the first and fifth metatarsal heads through constraints that allowed medial-lateral and distal-proximal translations and all the three pertaining rotations. These were named the'sphere on plane' constraints. The transverse bar F was then connected to bar L by a revolute joint (labelled D in Figure 2) which was oriented on the longitudinal axis of the foot. In this way, the pronation/supination and other movements out of the sagittal plane were not constrained by our measuring system. The rotation of bar L about the dorsi/plantarflexion axis was measured by revolute joint A, and was defined as  
Figure 1: The foot model. The different bones are coloured differently: pink the medial side of the foot (first three rays); blue/green the lateral side (4 th and 5 th rays); orange the astragalus; green/brown the calcaneus; blue/violet the tibia and peroneus. The linear actuators represent the muscles: pink the soleus; red the gastrocnemius and the tibialis posterior; green the flexor halluclus longus; dark green the flexor digitorum longus; light blue the tibialis anterior, and orange the extensor digitorum longus.  
the 'forefoot dorsiflexion' angle. The rotation of transverse bar F about the longitudinal axis of the foot was measured by revolute joint D, and was named the 'forefoot supination' angle.
* Talotibial rotation angle. A bar labelled T was hinged to revolute joint A and connected to the talus through a'sphere on plane' constraint (see above). Bar T acts as a reference axis for the talus. Revolute joint A provided us with the talotibial rotation angle.
* First metatarsus-talus rotation angle. A mediolateral axis passes through the centre of the talonavicular joint (talonavicular axis). Revolute joint C (see Figure 2) was designed to measure the dorsi/plantarflexion angle of the first metatararsal bone in relation to the reference axis of the talus (parallel to bar T). A bar (labelled M in Figure 2) was hinged to revolute joint C and connected to the first metatararsal bone by a sphere on plane constraint. The angle measured by revolute joint C was named the 'first metatarsus-talus' rotation angle.
* Calcaneus inversion/eversion angle. The axis of rotation of the taloclaneal joint, the Henke axis [34], was identified as an axis passing through the superior part of the talus and the lateral tuberosity of the calcaneus. When the foot was on the ground, the taloclaneal axis was oriented at 42\({}^{\circ}\) over the horizontal plane and 16\({}^{\circ}\) medially about the longitudinal foot axis. The corresponding revolute joint (labelled B in Figure 2) was fixed to the talus and provided us with the relative rotation of the calcaneus about the talus (the calcaneus inversion/eversion angle).