By Leonardo Sciascia

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4) and (5). The vector of the external forces Fext is given by: where: Fext = F + Fgrav (7) [ ]T F = F x Fy 0 0 0 0 0 0 (8) is the vector containing the Cartesian components of the forces acting on the handle axis (point P) and [ ]T Fgrav = 0 0 0 −M2 g 0 0 −M1 g 0 (9) is the vector containing the weights of the limbs. Note that the components of the external forces must be inserted in the positions corresponding to the coordinates deﬁned in the vector S. Substituting Eq. (7) into Eq. (1) and introducing the gravity vector G(q) = −JeT Fgrav we obtain: ̇ + G(q) − JeT F = ???? Ms (q)q̈ + C(q, q) (10) Since only the ﬁrst two components of the vector F are not null, the product JeT F can be rewritten in the form J T Fh , where Fh = [Fx Fy ]T indicates the vector of the forces acting on the handle axis (point P), and J is the reduced Jacobian matrix, given by the following expression: [ J(????, ????) = ????S1 ????S1 ???????? ???????? ????S2 ????S2 ???????? ???????? ] [ = ????xP ????xP ???????? ???????? ????yP ????yP ???????? ???????? ] (11) 36 G.

2. The subject was asked to perform the passive tests three times and the results containing the lowest error was selected. This error was driven by comparing the measured force and the estimated force applied on the handle, as well as drawing comparisons between the torques generated by dynamic eﬀects and the muscles. The P vector of this selected result was later used in active tests calculations. 969486 Dynamic Analysis of Handcycling: Mathematical Modelling . . 39 Fig. 2 Comparing the x component (a) and y component (b) of the estimated (Fxes , Fyes ) and measured forces (Fx , Fy ) during passive tests Fig.

The parameters a, l and h deﬁne the geometry of the base platform, while f and b describe the geometry of the moving platform by referring to Table 1 and Fig. 3a, b. The actuators are described by their total lengths sb (rear), sf (front), Fig. 1 Kinematic chains for parallel mechanisms: a Linear Delta robot; b ﬁrst proposed chain; c second proposed chain (lateral chain) (R is for revolute joint, P is for prismatic joint and U is for universal joint, and the actuated joints are underlined) A Kinematic Solution of a Novel Leg Mechanism … 43 Fig.