Perform an intrinsic rotation sequence about the Y and then Z axes

intrinsic_rotation_template.py

from sympy import symbols, cos, sin, pi, sqrt
from sympy.matrices import Matrix

### Create symbols for joint variables
q1, q2 = symbols('q1:3')

# Create a symbolic matrix representing an intrinsic sequence of rotations 
# about the Y and then Z axes. Let the rotation about the Y axis be described
# by q1 and the rotation about Z by q2. 

# Replace R_y and R_z with the appropriate (symbolic) elementary rotation matrices 

R_y = Matrix([[ cos(q1),        0,  sin(q1)],
              [       0,        1,        0],
              [-sin(q1),        0,  cos(q1)]])

R_z = Matrix([[ cos(q2), -sin(q2),        0],
              [ sin(q2),  cos(q2),        0],
              [ 0,              0,        1]])  
# and then compute YZ_intrinsic
YZ_intrinsic_sym = R_y * R_z

# Numerically evaluate YZ_intrinsic assuming:
   # q1 = 45 degrees and q2 = 60 degrees. 
   # NOTE: Trigonometric functions in Python assume the input is in radians!  

print("Rotation about the Y-axis by 45-degrees and then about the Z-axis by 60-degrees")
YZ_intrinsic_num = YZ_intrinsic_sym.evalf(subs={q1: pi/4, q2: pi/3})

On intrinisic sequences of rotations the subsequent elementary rotations are post-multiplied