PowerPoint PresentationPYTHON LAB PROJECT: SPHERICAL MANIPULATOR (2 DOF) MODELINGDR. ERIC CHOU XXXXXXXXXXIEEE SENIOR MEMBERIntroduction to RoboticsManipulation and...

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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, θ2

2) 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.



PowerPoint Presentation PYTHON LAB PROJECT: SPHERICAL MANIPULATOR (2 DOF) MODELING DR. ERIC CHOU IEEE SENIOR MEMBER Introduction to Robotics Manipulation and Programming Unit 2: Kinematics 2 DOF Spherical Robot Arm Modeling Inverse Kinematics a1 a2 a3 θ1 θ2 Problem: 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, θ2 2) 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.
Answered 2 days AfterNov 16, 2022

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

Baljit answered on Nov 18 2022
53 Votes
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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<=2 and x1>=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,...
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