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Robotics_assignment.py
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Robotics_assignment.py
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###################################
## Robotics Assignment
## Author : Jash Shah
###################################
from sympy import *
Q1 = Matrix([
[0,-1,0,0],
[1,0,0,0],
[0,0,0,0],
[0,0,0,0]
])
Q2 = Q1
#########################################3
var('m1 L1 m2 L2 a b')
a = m1*L1
b = m2*L2
I1 = Matrix([
[a*L1/3, 0, 0, -a/2],
[0, 0, 0, 0],
[0, 0, 0, 0],
[-a/2, 0, 0, m1]
])
I2 = Matrix([
[b*L2/3, 0, 0, -b/2],
[0, 0, 0, 0],
[0, 0, 0, 0],
[-b/2, 0, 0, m2]
])
##############################################
var('X1 X2')
var('S1 C1 S2 C2')
S1 = sin(X1)
S2 = sin(X2)
C1 = cos(X1)
C2 = cos(X2)
d11 = Matrix([
[-S1, 0, C1, -L1*S1],
[C1, 0, S1, C1*L1],
[0, 0, 0, 0],
[0, 0, 0, 0]
])
d12 = Matrix([
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0]
])
d21 = Matrix([
[-S1*C2, S1*S2, C1, ((-L2*S1*C2) - (L1*S1))],
[C2*C1, -C1*S2, S1, ((L2*C2*C1) + (L1*C1))],
[0,0,0,0],
[0,0,0,0]
])
d22 = Matrix([
[-C1*S2, -C1*C2, 0, -L2*C1*S2],
[-S1*S2, -S1*C2, 0, -L2*S1*S2],
[C2, -S2, 0, L2*C2],
[0, 0, 0, 0]
])
#####################################################
M11 = ( ( d11.multiply(I1) ).multiply(d11.T) ) + ( ( d21.multiply(I2)).multiply(d21.T) )
M22 = ( d22.multiply(I2) ).multiply(d22.T)
M21 = ( d22.multiply(I2) ).multiply(d21.T)
M12 = M21
print( "\n M11 = \n\n", trigsimp(trace(M11) ))
print( "\n M21 = \n\n", trigsimp(trace(M21)) )
print( "\n M12 = \n\n", trigsimp(trace(M12)) )
print( "\n M22 = \n\n", trigsimp(trace(M22)) )
##############################################################################
T01 = Matrix([
[C1, 0, S1, L1*C1],
[S1, 0, -C1, L1*S1],
[0, 1, 0, 0],
[0, 0, 0, 1]
])
T12 = Matrix([
[C2, -S2, 0, L2*C2],
[S2, C2, 0, L2*S2],
[0, 0, 1, 0],
[0, 0, 0, 1]
])
T02 = T01.multiply(T12)
temp = diff(d22,X2)
temp1 = diff(d21,X1)
#####################################################################################
h122 = temp@I2@d21.T
h211 = temp1@I2@d22.T
h221 = temp1@I2@d22.T
h121 = temp1@I2@d21.T
print( "\n h122 = \n\n", trigsimp(trace(h122)) )
print( "\n h211 = \n\n", trigsimp(trace(h211)) )
print( "\n h221 = \n\n", trigsimp(trace(h221)) )
print( "\n h121 = \n\n", trigsimp(trace(h121)) )
######################################################################################