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BasicFunc.py
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293 lines (263 loc) · 15.7 KB
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from math import *
import cmath
#
# Fixed parameters
#
h = 0.0001 # time interval for step-by-step calculation (sec)
#
# Physical parameters
#
g_vertical = 9.806 # (m/sec^2)
#
# Other parameters
#
PI = 3.141592653589793
norm = 270.0 # (degree)
nrom_rad = norm*PI/180.0 # (rad)
#
# sub-functions
#
def func_Q_alpha(t, tau, Set_Q_alpha):
ans_Q_alpha = Set_Q_alpha*(1-exp(-1*t/tau))
return ans_Q_alpha
def func_Q_beta(t, tau, Set_Q_beta, theta, Set_theta, t0):
if (theta > Set_theta):
ans_Q_beta = 0.0
else:
ans_Q_beta = Set_Q_beta*(1-exp(-1*(t-t0)/tau))
return ans_Q_beta
def club_para(M_C_head, M_C_shaft, L_C_head, L_C_shaft):
M_C = M_C_head + M_C_shaft
L = L_C_head/2.0 + L_C_shaft
L_eff = (M_C_head*(L_C_shaft + L_C_head/2.0) + M_C_shaft*L_C_shaft/2.0)/M_C
S_C = M_C*L_eff
I = M_C*L_eff**2
return M_C, L, S_C, I
def func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, \
J, S_A, R, \
set_Q_alpha, \
alpha_dot_rad, \
beta_rad, beta_dot_rad, beta_ddot_rad, \
theta_rad):
g = g_vertical*sin(phi*PI/180.0) - a_y
alpha_part1 = J + I + M_C*R**2 + 2*R*S_C*cos(beta_rad)
alpha_part2 = (I + R*S_C*cos(beta_rad))*beta_ddot_rad
alpha_part3 = -1*(beta_dot_rad**2 - 2*alpha_dot_rad*beta_dot_rad)*R*S_C*sin(beta_rad)
alpha_part4 = S_C*(g*sin(theta_rad+beta_rad) - a_x*cos(theta_rad+beta_rad))
alpha_part5 = (S_A + M_C*R)*(g*sin(theta_rad) - a_x*cos(theta_rad))
alpha_ddot_ans = (1/alpha_part1)*(set_Q_alpha + alpha_part2 + alpha_part3 + alpha_part4 + alpha_part5)
return alpha_ddot_ans
def func_beta_ddot(a_x, a_y, phi, I, S_C, \
R, set_Q_beta, \
alpha_dot_rad, alpha_ddot_rad, \
beta_rad, \
theta_rad):
g = g_vertical*sin(phi*PI/180.0) - a_y
beta_part1 = (I + R*S_C*cos(beta_rad))*alpha_ddot_rad
beta_part2 = -1*alpha_dot_rad**2*R*S_C*sin(beta_rad)
beta_part3 = -1*S_C*(g*sin(theta_rad+beta_rad) - a_x*cos(theta_rad+beta_rad))
beta_ddot_ans = (1/I)*(set_Q_beta + beta_part1 + beta_part2 + beta_part3)
return beta_ddot_ans
def func_VC(alpha_dot_rad, beta_rad, beta_dot_rad, R, L):
VC_part1 = (R**2 + L**2 + 2*R*L*cos(beta_rad))*alpha_dot_rad**2
VC_part2 = L**2*beta_dot_rad**2
VC_part3 = -2*(L**2 + R*L*cos(beta_rad))*alpha_dot_rad*beta_dot_rad
VC_sum = VC_part1 + VC_part2 + VC_part3
if (VC_sum >= 0):
return sqrt(VC_sum)
else:
return 'V_C value is not a real number!'
def func_general_xy(o_x, o_y, angle, length):
ans_general_x = o_x + cos(angle)*length
ans_general_y = o_y + sin(angle)*length
return ans_general_x, ans_general_y
def func_arm_xy(theta_rad, R):
ans_arm_x = cos(nrom_rad-theta_rad)*R
ans_arm_y = sin(nrom_rad-theta_rad)*R
return ans_arm_x, ans_arm_y
def func_club_xy(theta_rad, beta_rad, R, L):
ans_club_x = cos(nrom_rad-theta_rad)*R + cos(nrom_rad-theta_rad-beta_rad)*L
ans_club_y = sin(nrom_rad-theta_rad)*R + sin(nrom_rad-theta_rad-beta_rad)*L
return ans_club_x, ans_club_y
def func_O_xy(t):
ans_O_x = 0.0
ans_O_y = 0.0
return ans_O_x, ans_O_y
def func_VC_xy(O_x, O_y, arm_x, arm_y, club_x, club_y, alpha_dot_rad, beta_rad, beta_dot_rad, t, R, L):
vec_r_x = club_x - O_x
vec_r_y = club_y - O_y
vec_r_x_bot = -1*(club_y - O_y)
vec_r_y_bot = club_x - O_x
vec_r_x_bot_hat = -1*(club_y - O_y)/sqrt(vec_r_x_bot**2+vec_r_y_bot**2)
vec_r_y_bot_hat = (club_x - O_x)/sqrt(vec_r_x_bot**2+vec_r_y_bot**2)
vec_L_x = club_x - arm_x
vec_L_y = club_y - arm_y
vec_L_x_bot = -1*(club_y - arm_y)
vec_L_y_bot = club_x - arm_x
vec_L_x_bot_hat = -1*(club_y - arm_y)/sqrt(vec_L_x_bot**2+vec_L_y_bot**2)
vec_L_y_bot_hat = (club_x - arm_x)/sqrt(vec_L_x_bot**2+vec_L_y_bot**2)
r = sqrt(R**2 + L**2 + 2*R*L*cos(beta_rad))
vec_VC_x = r*alpha_dot_rad*vec_r_x_bot_hat - L*beta_dot_rad*vec_L_x_bot_hat
vec_VC_y = r*alpha_dot_rad*vec_r_y_bot_hat - L*beta_dot_rad*vec_L_y_bot_hat
vec_VC_check = sqrt(vec_VC_x**2 + vec_VC_y**2)
vec_VC_angle_rad_tmp = cmath.phase(complex(vec_VC_x, vec_VC_y))
if (PI/2 <= vec_VC_angle_rad_tmp <= PI):
vec_VC_angle_rad = vec_VC_angle_rad_tmp - 2*PI
else:
vec_VC_angle_rad = vec_VC_angle_rad_tmp
return vec_VC_x, vec_VC_y, vec_VC_angle_rad, vec_VC_check
def RK4_I(a_x, a_y, phi, I, S_C, M_C, \
J, S_A, R, \
set_Q_alpha, set_Q_beta, \
alpha_rad, alpha_dot_rad, alpha_ddot_rad, \
beta_rad, beta_dot_rad, beta_ddot_rad, \
theta_rad):
#----------------------------------------------------------------------------------------------------------------
k1 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad, beta_rad, beta_dot_rad, beta_ddot_rad, theta_rad)
q1 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad, alpha_ddot_rad, beta_rad, theta_rad)
#----------------------------------------------------------------------------------------------------------------
k2 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad + (1/2)*k1*h, beta_rad, beta_dot_rad + (1/2)*q1*h, beta_ddot_rad, theta_rad)
q2 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad + (1/2)*k1*h, alpha_ddot_rad, beta_rad, theta_rad)
#----------------------------------------------------------------------------------------------------------------
k3 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad + (1/2)*k2*h, beta_rad, beta_dot_rad + (1/2)*q2*h, beta_ddot_rad, theta_rad)
q3 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad + (1/2)*k2*h, alpha_ddot_rad, beta_rad, theta_rad)
#----------------------------------------------------------------------------------------------------------------
k4 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad + k3*h, beta_rad, beta_dot_rad + q3*h, beta_ddot_rad, theta_rad)
q4 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad + k3*h, alpha_ddot_rad, beta_rad, theta_rad)
#----------------------------------------------------------------------------------------------------------------
alpha_dot_rad_n1 = alpha_dot_rad + (h/6)*(k1 + 2*k2 + 2*k3 + k4)
beta_dot_rad_n1 = beta_dot_rad + (h/6)*(q1 + 2*q2 + 2*q3 + q4)
#----------------------------------------------------------------------------------------------------------------
alpha_rad_n1 = alpha_rad + alpha_dot_rad_n1*h
beta_rad_n1 = beta_rad + beta_dot_rad_n1*h
#----------------------------------------------------------------------------------------------------------------
return alpha_rad_n1, alpha_dot_rad_n1, k1, beta_rad_n1, beta_dot_rad_n1, q1
def RK4_II(a_x, a_y, phi, I, S_C, M_C, \
J, S_A, R, \
set_Q_alpha, set_Q_beta, \
alpha_rad, alpha_dot_rad, \
beta_rad, beta_dot_rad, beta_ddot_rad, \
theta_rad):
#----------------------------------------------------------------------------------------------------------------
k1 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad, beta_rad, beta_dot_rad, beta_ddot_rad, theta_rad)
q1 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad, k1, beta_rad, theta_rad)
#----------------------------------------------------------------------------------------------------------------
k2 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad + (1/2)*k1*h, beta_rad, beta_dot_rad + (1/2)*q1*h, q1, theta_rad)
q2 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad + (1/2)*k1*h, k2, beta_rad, theta_rad)
#----------------------------------------------------------------------------------------------------------------
k3 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad + (1/2)*k2*h, beta_rad, beta_dot_rad + (1/2)*q2*h, q2, theta_rad)
q3 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad + (1/2)*k2*h, k3, beta_rad, theta_rad)
#----------------------------------------------------------------------------------------------------------------
k4 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad + k3*h, beta_rad, beta_dot_rad + q3*h, q3, theta_rad)
q4 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad + k3*h, k4, beta_rad, theta_rad)
#----------------------------------------------------------------------------------------------------------------
alpha_dot_rad_n1 = alpha_dot_rad + (h/6)*(k1 + 2*k2 + 2*k3 + k4)
beta_dot_rad_n1 = beta_dot_rad + (h/6)*(q1 + 2*q2 + 2*q3 + q4)
#----------------------------------------------------------------------------------------------------------------
alpha_rad_n1 = alpha_rad + alpha_dot_rad_n1*h
beta_rad_n1 = beta_rad + beta_dot_rad_n1*h
#----------------------------------------------------------------------------------------------------------------
return alpha_rad_n1, alpha_dot_rad_n1, k1, beta_rad_n1, beta_dot_rad_n1, q1
def RK4_III(a_x, a_y, phi, I, S_C, M_C, \
J, S_A, R, \
set_Q_alpha, set_Q_beta, \
alpha_rad, alpha_dot_rad, alpha_ddot_rad, \
beta_rad, beta_dot_rad, \
theta_rad):
#----------------------------------------------------------------------------------------------------------------
q1 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad, alpha_ddot_rad, beta_rad, theta_rad)
k1 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad, beta_rad, beta_dot_rad, q1, theta_rad)
#----------------------------------------------------------------------------------------------------------------
q2 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad + (1/2)*k1*h, k1, beta_rad, theta_rad)
k2 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad + (1/2)*k1*h, beta_rad, beta_dot_rad + (1/2)*q1*h, q2, theta_rad)
#----------------------------------------------------------------------------------------------------------------
q3 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad + (1/2)*k2*h, k2, beta_rad, theta_rad)
k3 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad + (1/2)*k2*h, beta_rad, beta_dot_rad + (1/2)*q2*h, q3, theta_rad)
#----------------------------------------------------------------------------------------------------------------
q4 = func_beta_ddot(a_x, a_y, phi, I, S_C, R, set_Q_beta, alpha_dot_rad + k3*h, k3, beta_rad, theta_rad)
k4 = func_alpha_ddot(a_x, a_y, phi, I, S_C, M_C, J, S_A, R, set_Q_alpha, alpha_dot_rad + k3*h, beta_rad, beta_dot_rad + q3*h, q4, theta_rad)
#----------------------------------------------------------------------------------------------------------------
alpha_dot_rad_n1 = alpha_dot_rad + (h/6)*(k1 + 2*k2 + 2*k3 + k4)
beta_dot_rad_n1 = beta_dot_rad + (h/6)*(q1 + 2*q2 + 2*q3 + q4)
#----------------------------------------------------------------------------------------------------------------
alpha_rad_n1 = alpha_rad + alpha_dot_rad_n1*h
beta_rad_n1 = beta_rad + beta_dot_rad_n1*h
#----------------------------------------------------------------------------------------------------------------
return alpha_rad_n1, alpha_dot_rad_n1, k1, beta_rad_n1, beta_dot_rad_n1, q1
def Ball_velocity(V_head, M_head, M_ball, COR):
ans_Ball_velocity = V_head*(1+COR)*M_head/(M_ball+M_head)
return ans_Ball_velocity
def inner_angle_TypeI(R_S, R_A):
inner_angle_TypeI_ans = acos(R_S/R_A)
return inner_angle_TypeI_ans
def arm_length_TypeI(R_S, R_A):
arm_length_TypeI_ans = sqrt(R_A**2-R_S**2)
return arm_length_TypeI_ans
def Integrate1(R_S, inner_angle_original, r_A):
inner_angle = abs(inner_angle_original)
Integrate1_ans = (R_S**2)*r_A + (r_A**3)/3 - R_S*(r_A**2)*cos(inner_angle)
return Integrate1_ans
def Integrate2(R_S, inner_angle_original, r_A):
inner_angle = abs(inner_angle_original)
Integrate2_part1 = (r_A-R_S*cos(inner_angle))/(R_S*sin(inner_angle))
Integrate2_part2 = sqrt(R_S**2+r_A**2-2*R_S*r_A*cos(inner_angle))
#Integrate2_part3 = (R_S**2)*(sin(inner_angle)**2)*np.arcsinh(Integrate2_part1)
Integrate2_part3 = (R_S**2)*(sin(inner_angle)**2)*asinh(Integrate2_part1)
Integrate2_part4 = (r_A-R_S*cos(inner_angle))*Integrate2_part2
Integrate2_ans = Integrate2_part3 + Integrate2_part4
return Integrate2_ans
def J_TypeI(R_S, R_A, rho_S, rho_A1, rho_A2, inner_angle):
J_TypeI_part1 = 2*rho_A1*Integrate1(R_S, inner_angle, R_A/2) - 0.0
J_TypeI_part2 = 2*rho_A2*Integrate1(R_S, inner_angle, R_A) - 2*rho_A2*Integrate1(R_S, inner_angle, R_A/2)
J_TypeI_part3 = 2*rho_S*(R_S**3)/3
J_TypeI_ans = J_TypeI_part1 + J_TypeI_part2 + J_TypeI_part3
return J_TypeI_ans
def S_A_TypeI(R_S, R_A, rho_S, rho_A1, rho_A2, inner_angle):
S_A_TypeI_part1 = rho_A1*(Integrate2(R_S, inner_angle, R_A/2)-Integrate2(R_S, inner_angle, 0.0))
S_A_TypeI_part2 = rho_A2*(Integrate2(R_S, inner_angle, R_A)-Integrate2(R_S, inner_angle, R_A/2))
S_A_TypeI_part3 = rho_S*R_S**2 - 0.0
S_A_TypeI_ans = S_A_TypeI_part1 + S_A_TypeI_part2 + S_A_TypeI_part3
return S_A_TypeI_ans
def bending_arm_para(R_S, R_A, bending_angle):
R_Ap = R_A*sin(bending_angle/2)
mu = PI/2 - bending_angle/2
delta_part1 = (R_Ap**2 - R_A**2 - (2*R_S)**2)/(-2*(2*R_S)*R_A)
delta = acos(delta_part1)
lambda1_part1 = (R_A**2 - R_Ap**2 - (2*R_S)**2)/(-2*(2*R_S)*R_Ap)
lambda1 = acos(lambda1_part1) - mu
R_eff = sqrt(R_A**2 + R_S**2 - 2*R_A*R_S*cos(delta))
epsilon_part1 = (R_S**2 - R_Ap**2 - R_eff**2)/(-2*R_Ap*R_eff)
epsilon = acos(epsilon_part1)
sigma = mu - epsilon
return R_eff, delta, lambda1, sigma
def bending_arm_angle_min(R_S, R_A):
L1 = (R_A-2*R_S)/2
L2 = R_A/2
bending_arm_angle_min_ans_tmp = 2*asin(L1/L2)
if (bending_arm_angle_min_ans_tmp < PI/2):
bending_arm_angle_min_ans = PI/2
else:
bending_arm_angle_min_ans = bending_arm_angle_min_ans_tmp
return bending_arm_angle_min_ans
def bending_arm_angle(theta_ini, alpha, omega_ini):
bending_arm_angle_ans = omega_ini + (alpha/theta_ini)*(PI-omega_ini)
if (bending_arm_angle_ans <= PI):
return bending_arm_angle_ans
else:
return PI
def J_TypeII(R_S, R_A, rho_S, rho_A1, rho_A2, R_eff, inner_angle1, inner_angle2, inner_angle3):
J_TypeII_part1 = rho_A1*Integrate1(R_S, inner_angle1, R_A/2) - 0.0
J_TypeII_part2 = rho_A2*Integrate1(R_S, inner_angle1, R_A) - rho_A2*Integrate1(R_S, inner_angle1, R_A/2)
J_TypeII_part3 = rho_A1*Integrate1(R_S, inner_angle2, R_A/2) - 0.0
J_TypeII_part4 = rho_A2*Integrate1(R_eff, inner_angle3, R_A/2) - 0.0
J_TypeII_part5 = 2*rho_S*(R_S**3)/3
J_TypeII_ans = J_TypeII_part1 + J_TypeII_part2 + J_TypeII_part3 + J_TypeII_part4 + J_TypeII_part5
return J_TypeII_ans
def S_A_TypeII(R_S, R_A, rho_S, rho_A1, rho_A2, R_eff, inner_angle1, inner_angle2, inner_angle3):
S_A_TypeII_part1 = (rho_A1/2)*(Integrate2(R_S, inner_angle1, R_A/2)-Integrate2(R_S, inner_angle1, 0.0))
S_A_TypeII_part2 = (rho_A2/2)*(Integrate2(R_S, inner_angle1, R_A)-Integrate2(R_S, inner_angle1, R_A/2))
S_A_TypeII_part3 = (rho_A1/2)*(Integrate2(R_S, inner_angle2, R_A/2)-Integrate2(R_S, inner_angle2, 0.0))
S_A_TypeII_part4 = (rho_A2/2)*(Integrate2(R_eff, inner_angle3, R_A/2)-Integrate2(R_eff, inner_angle3, 0.0))
S_A_TypeII_part5 = rho_S*R_S**2 - 0.0
S_A_TypeII_ans = S_A_TypeII_part1 + S_A_TypeII_part2 + S_A_TypeII_part3 + S_A_TypeII_part4 + S_A_TypeII_part5
return S_A_TypeII_ans