Tional society of biomechanics (ISB) [24], we establish the coordinate technique attached to a limb on the proximal joint, and all of the coordinate systems are the right-hand Cartesian coordinates. As shown in Figure 4, the limbs from the pelvis, upper leg, reduce leg, and foot with the left leg are denoted because the rod L1 , L2 , L3 , and L4 , respectively, as well as the coordinate method attached to each and every limb is denoted as L1 , L2 , L3 , L4 . In most human motions, the pelvis generally makes only translational motion with out rotation; as a result, within the case of only calculating the joint angles, the L1 rod can be considered as a fixed rod.A LyL2 z L2 JHx Ly LL2 BOz LJKxLC LyL4 x LJAND LrJKzLFigure 4. Structural diagram of human reduce limb.As shown in Figure 5a, L2 is established at JH . Make the standard line of r JK through JH , as well as the foot point is N. The y-axes path from the attached coordinate system is from N to JH . The z-axes parallel to the knee joint rotation axis along with the path is left leg to YM511 medchemexpress suitable leg. The x-axes are perpendicular for the y- and z-axes. In Figure 5b, the vertical line of your knee joint is produced via the point J A , as well as the vertical point is O, L3 is established at O. The y-axes direction is from J A to O. The z-axes coincides using the knee joint axis, along with the path is definitely the left leg to suitable leg. The x-axes are perpendicular to the y and z-axes, L4 is established at J A . At the initial stage, L1 and L2 coincide, and L3 and L4 are parallel.Sensors 2021, 21,11 ofy LJHx LLVJH, ByLBVJK, B VBNz Lz LJKOVJK, CxLVCOJKrJKCVJA, Cy LJANLx Lr(a)JKz L(b)Figure five. Structure diagram of limbs and position vector of each and every joint. (a) Limb L2 ; (b) Limb L3 .The attitude transformation between two adjacent sensors is defined by Equation (30).A R B (t) = ( R A (t)) T R B (t), B RC (t) = ( R B (t)) T RC (t), Og Og Og Og(30)RC (t) = ( RC (t)) T R D (t), DA where R B would be the attitude transformation matrix involving A and B. The attitude transforB mation matrix amongst B and C is denoted as RC . The attitude transformation matrix C in between C and D is denoted as R D . The attitude transformation matrix of every single IMUOgOgrelative to the global coordinate technique at time t is denoted as RS , S A, B, C, D. It can be worth noting that only the sensor coordinate program Os is time-dependent, resulting in RS altering with time and Og is not time-dependent. We analyze the fusion approach in detail in Section four.three. When the human body has not started motion capture and stands NPS 2390 Purity & Documentation nonetheless, A B the attitude transformations involving IMUs are denoted by R B (0), RC (0), RC (0). D Based on the analysis in Section 3, the V JH , B , V JK , B , V JK , C , V JA , C , V JA , D , r JK , B , and r JK , C could be obtained. As shown in Figure 5a,b, V BN and V CO ought to be calculated to receive the coordinate method attached to each limb. Establishing the equation from the knee joint axis by Equation (31). x + x2 y + y2 z + z2 = = , rx ry rzT OgOg(31)exactly where [ x2 , y2 , z2 ] T denote the coordinates of V JH , B and [ x3 , y3 , z3 ] T denote the coordinates of V JK , B . r x , ry , rz denote the coordinates of r JK , B . [ x, y, z] T is any point on a line, and point N is on this line. Assume that the coordinates of V BN are [ a, b, c] T , the equation of knee joint axis by Equation (32). a + x2 b + y2 c + z2 = = rx ry rz The typical line of r JK may be expressed by Equation (33). r x ( a + x3 ) + r y ( b + y3 ) + r z ( a + z3 ) = 0 (33) (32)Based on Equa.
