Report - PEER - University of California, Berkeley

3.3 Equilibrium EquationsEquilibrium should be satisfied. Equilibrium equations are established for each freebody for horizontal and vertical directional forces as well as moment for J-mode. Equilibriumequations are established for axial force and moment for B-mode. Compatibilitycondition may not be necessarily satisfied.3.3.1 J-modeBy considering the symmetry of the free body, six equilibrium equations are necessaryto define the equilibrium of the knee joint. However number of independent equilibriumequations is five for each case (a) under closing moment shown in Fig. 4(d), and(b) under opening moment shown in Fig. 4(f). In the case under closing moment, theindependent equilibrium equations are from Eqns. (1) to (5),– T 2– T 3+ C 2+ C 3– T 5– N = 0(segment BOD: x-direction) (1)– T 1– T 4+ C 1+ C 2– T 5= 0T 1– T 2– C 2+ C 3– V = 0(segment AOB: y-direction) (2)(segment BOD: y-direction) (3)1--jD( 2T2 4– T 1– T 3)C 22------- Ctσ 1D C 1+ – ⎛ – ------- ⎞ = 0c⎝ tσ c⎠(segment AOB: moment) (4)1--jD( T2 1– 2T 2+ T 3)C 22– ------- Ctσ 3D C 3+ ⎛ – ------- ⎞c⎝ tσ c⎠– LV = 0(segment BOD: moment) (5)whereas, for the case under opening moment, equilibrium equations are Eqns. (6) to(10).– T 2– T 3+ C 5+ C 6– T 5+ N = 0(free body BOD: x-direction) (6)– T 1– T 4+ C 4+ C 5– T 5= 0T 1– T 2– C 5+ C 6+ V = 0(free body AOB: y-direction) (7)(free body BOD: y-direction) (8)1--jD( 2T2 4– T 1– T 3)C 42– ------- Ctσ 5D C 5+ ⎛ – ------- ⎞ = 0c⎝ tσ c⎠(free body AOB: moment) (9)1--jD( T2 1– 2T 2+ T 3)C 62------- Ctσ 5D C 5+ – ⎛ – ------- ⎞ + LV = 0c⎝ tσ c⎠(free body BOD: moment) (10)462