🔒 solving system of linear equations but the output is some function I can plot

[icy scaffold]

I'm trying to solve a system of linear equations, matrix A is constant and stays the same, matrix x is the output matrix, where each element of the output array is a array itself consisting of values that will be plotted with theta_2 and matrix b which is what varies.

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@icy scaffold

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[icy scaffold]

def omega_3_computation(a, b, omega_2, theta_4, theta_3, theta_2):
    numerator = a * omega_2 * np.sin(theta_4 - theta_2)
    denominator = b * np.sin(theta_3 - theta_4)
    omega_3 = numerator / denominator
    return omega_3


def omega_4_computation(a, c, omega_2, theta_4, theta_3, theta_2):
    numerator = a * omega_2 * np.sin(theta_2 - theta_3)
    denominator = c * np.sin(theta_4 - theta_3)
    omega_4 = numerator / denominator
    return omega_4


def m_A_computation(r_in, r_out, c, a, theta_4, theta_3, theta_2):
    numerator = c * np.sin(theta_4 - theta_3) * r_in
    denominator = a * np.sin(theta_2 - theta_3) * r_out
    m_A = np.abs(numerator / denominator)
    return m_A

def fourbarlinkage():
    a = 6.5
    b = 5
    c = 7
    d = 3.25

    r_in = a
    r_out = c / 2

    omega_2 = 0
    alpha_2 = 10

    u = 3
    p = 9
    s = 2.5

    delta_2 = 0
    delta_3 = np.radians(300)
    delta_4 = 0

    # theta_2 = np.linspace(np.pi, 2 * np.pi, 300)
    theta_2 = np.radians(275)

    k_1 = d / a
    k_2 = d / c
    k_3 = (a**2 - b**2 + c**2 + d**2) / (2 * a * c)
    k_4 = d / b
    k_5 = (c**2 - d**2 - a**2 - b**2) / (2 * a * b)

    A = np.cos(theta_2) - k_1 - k_2 * np.cos(theta_2) + k_3
    B = -2 * np.sin(theta_2)
    C = k_1 - (k_2 + 1) * np.cos(theta_2) + k_3
    D = np.cos(theta_2) - k_1 + k_4 * np.cos(theta_2) + k_5
    E = -2 * np.sin(theta_2)
    F = k_1 + (k_4 - 1) * np.cos(theta_2) + k_5

    theta_3plus = 2 * np.atan(((-E + np.sqrt(E**2 - 4 * D * F)) / (2 * D)))
    theta_3minus = 2 * np.atan(((-E - np.sqrt(E**2 - 4 * D * F)) / (2 * D)))

    theta_4plus = 2 * np.atan(((-B + np.sqrt(B**2 - 4 * A * C)) / (2 * A)))
    theta_4minus = 2 * np.atan(((-B - np.sqrt(B**2 - 4 * A * C)) / (2 * A)))

    theta_3 = theta_3plus
    theta_4 = theta_4plus

    mu = np.abs(theta_4 - theta_3)

    omega_3 = omega_3_computation(a, b, omega_2, theta_4, theta_3, theta_2)
    omega_4 = omega_4_computation(a, c, omega_2, theta_4, theta_3, theta_2)

    m_A = m_A_computation(r_in, r_out, c, a, theta_4plus, theta_3minus, theta_2)

    A = c * np.sin(theta_4)
    B = b * np.sin(theta_3)
    C = (
        a * alpha_2 * np.sin(theta_2)
        + a * omega_2**2 * np.cos(theta_2)
        + b * omega_3**2 * np.cos(theta_3)
        - c * omega_4**2 * np.cos(theta_4)
    )
    D = c * np.cos(theta_4)
    E = b * np.cos(theta_3)
    F = (
        a * alpha_2 * np.cos(theta_2)
        - a * omega_2**2 * np.sin(theta_2)
        - b * omega_3**2 * np.sin(theta_3)
        + c * omega_4**2 * np.sin(theta_4)
    )

    alpha_3 = (C * D - A * F) / (A * E - B * D)
    alpha_4 = (C * E - B * F) / (A * E - B * D)

    A_S_x = -(
        s * alpha_2 * np.sin(theta_2 + delta_2)
        + s * omega_2**2 * np.cos(theta_2 + delta_2)
    )
    A_S_y = s * alpha_2 * np.cos(theta_2 + delta_2) - s * omega_2**2 * np.sin(
        theta_2 + delta_2
    )

    A_P_x = -(a * alpha_2 * np.sin(theta_2) + a * omega_2**2 * np.cos(theta_2)) - (
        p * alpha_3 * np.sin(theta_3 + delta_3)
        + p * omega_3**2 * np.cos(theta_3 + delta_3)
    )
    A_P_y = (a * alpha_2 * np.cos(theta_2) - a * omega_2**2 * np.sin(theta_2)) + (
        p * alpha_3 * np.cos(theta_3 + delta_3)
        - p * omega_3**2 * np.sin(theta_3 + delta_3)
    )

    A_U_x = -(
        u * alpha_4 * np.sin(theta_4 + delta_4)
        + u * omega_4**2 * np.cos(theta_4 + delta_4)
    )
    A_U_y = u * alpha_4 * np.cos(theta_4 + delta_4) - u * omega_4**2 * np.sin(
        theta_4 + delta_4
)

    R_12y = 3.164
    R_12x = .004
    R_32y = 3.336
    R_32x = .004
    R_23y = 0.003
    R_23x = 4.157
    R_43y = .843
    R_43x = 0.003
    R_34y = 3.56
    R_34x = .001
    R_14y = 3.544
    R_14x = .001

    m_2 = 0.0458
    m_3 = 0.0441
    m_4 = 0.0168

    R_P_3x = 0
    R_P_3y = 0
    R_P_4x = 0
    R_P_4y = 0

    a_G_2x = 0
    a_G_2y = 0
    a_G_3x = 0
    a_G_3y = 0
    a_G_4x = 0
    a_G_4y = 0

    I_G_2 = 0.0965890062111801
    I_G_3 = 0.377257826086957
    I_G_4 = 0.111371708074534

    F_P_3x = 0
    F_P_3y = 0
    F_P_4x = 0
    F_P_4y = 0
    T_3 = 0
    T_4 = 0

    

    b = np.array(
        [
            [m_2 * a_G_2x],
            [m_2 * a_G_2y],
            [I_G_2 * alpha_2],
            [m_3 * a_G_3x - F_P_3x],
            [m_3 * a_G_3y - F_P_3y],
            [I_G_3 * alpha_3 - (R_P_3x * F_P_3y - R_P_3y * F_P_3x) - T_3],
            [m_4 * a_G_4x - F_P_4x],
            [m_4 * a_G_4y - F_P_4y],
            [I_G_4 * alpha_4 - (R_P_4x * F_P_4y - R_P_4y * F_P_4x) - T_4],
        ],
    )

    A = np.array(
        [
            [1, 0, 1, 0, 0, 0, 0, 0, 0],
            [0, 1, 0, 1, 0, 0, 0, 0, 0],
            [-R_12y, R_12x, -R_32y, R_32x, 0, 0, 0, 0, 1],
            [0, 0, -1, 0, 1, 0, 0, 0, 0],
            [0, 0, 0, -1, 0, 1, 0, 0, 0],
            [0, 0, R_23y, -R_23x, -R_43y, R_43x, 0, 0, 0],
            [0, 0, 0, 0, -1, 0, 1, 0, 0],
            [0, 0, 0, 0, 0, -1, 0, 1, 0],
            [0, 0, 0, 0, R_34y, -R_34x, -R_14y, R_14x, 0],
        ]
    )
    print(A)
    print(b)
    X = np.linalg.solve(A,b)
    print('space')
    print(X)

[vagrant ocean]

@icy scaffold

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