PowerPoint PresentationPYTHON LAB PROJECT: SPHERICAL MANIPULATOR (2 DOF) MODELINGDR. ERIC CHOU ...

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PowerPoint PresentationPYTHON LAB PROJECT: SPHERICAL MANIPULATOR (2 DOF) MODELINGDR. ERIC CHOU                            XXXXXXXXXXIEEE SENIOR MEMBERIntroduction to RoboticsManipulation and ProgrammingUnit 2: Kinematics2 DOF Spherical Robot Arm ModelingInverse Kinematicsa1a2a3θ1θ2Problem: 1) Use Mathematical modeling to determine the workspace of this manipulator under all possible x, y, z, Given, a1, a2, and a3 are all 1.  All possible θ1, θ22) Given a point [x, y, z] within the workspace.  Find θ1, θ2 formulas.  Write them down in a paper. 3) Write a program to calculate these two angles for all given [x, y, z] with respect to frame 0.

Baljit · Accepted Answer

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from pylab import *
import numpy as np
 
def icos(a,b,c):
    t=arccos((a**2+b**2-c**2)/(2*a*b))
    return t
N=1000
a2=1
a3=1
x=[]
y=[]
for i in range(N):
    while True:
        x1=random()*4.01-2.0
        y1=random()*4.01-2.0
        r1=np.sqrt(x1**2+y1**2)
        if r1=0 and y1>=0:
            x.append(x1)
            y.append(y1)
            break
 
scatter(x,y)
r=[np.sqrt(x[i]**2+y[i]**2) for i in range(N)]
phi_1=[icos(a2,r[i],a3) for i in range(N)]
phi_2=[arctan(y[i]/x[i]) for i in range(N)]
phi_3=[icos(a2,a3,r[i]) for i in range(N)]
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[-1.8205253068390388, 42.38466107381963, -28.318381415131043, -61.

PowerPoint Presentation PYTHON LAB PROJECT: SPHERICAL MANIPULATOR (2 DOF) MODELING DR. ERIC CHOU XXXXXXXXXXIEEE SENIOR MEMBER Introduction to Robotics Manipulation and...

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