1) Use Mathematical modeling to determine the workspace of this manipulator under all possible x, y,...

Question

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, θ_2. Submit the mathematical description of the workspace (.pdf, .jpeg, .png are acceptable).

2) Given a point [x, y, z] within the workspace.Find θ₁, θ₂formulas.Write them down on paper.

Mathematical Equations for θ₁, θ_2.Submit the mathematical description of the workspace (.pdf, .jpeg, .png are acceptable).

3) Write a program to calculate these two angles for all given [x, y, z] with respect to frame 0.

.py files

Baljit · Accepted Answer

Graphical Representation of Given Manipulator is 
Figure 1
1.  For given manipulator
Our homogeneous Transformation Matrix is
So
Here C=cos and S=sin
p= 
Which implies 
 x=
 y=
  
For the Workspace of Given Manipulator  
2.

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. Submit the mathematical description of the...

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