1) All prismatic manipulator is a simple manipulator. You can read its Jacobian matrix by inspecting...

Question

1) All prismatic manipulator is a simple manipulator. You can read its Jacobian matrix by inspecting the coordinates. Please derivate the Inverse Jacobian Matrix for this manipulator, write them down on paper, and submit it by image file or word .docx, or .pdf files.Show all equations for the derivative functions

$d 1 " class="formula-container wants-props-update" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); line-height: inherit; display: inline-block;"> d 1 " class="Wirisformula" role="img" alt="d subscript 1" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); max-width: 100%; height: 30px; display: inline; vertical-align: -14px; line-height: inherit; max-height: 31.25rem; width: 17px;"> $ ,

$d 2 " class="formula-container wants-props-update" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); line-height: inherit; display: inline-block;"> d 2 " class="Wirisformula" role="img" alt="d subscript 2" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); max-width: 100%; height: 30px; display: inline; vertical-align: -14px; line-height: inherit; max-height: 31.25rem; width: 17px;"> $ ,

$d 3 " class="formula-container wants-props-update" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); line-height: inherit; display: inline-block;"> d 3 " class="Wirisformula" role="img" alt="d subscript 3" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); max-width: 100%; height: 30px; display: inline; vertical-align: -14px; line-height: inherit; max-height: 31.25rem; width: 17px;"> $ .Given the path equations.

2) Write a Python program to calculate a numerical result for this prismatic manipulator.All

$a 1 " class="formula-container wants-props-update" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); line-height: inherit; display: inline-block;"> a 1 " class="Wirisformula" role="img" alt="a subscript 1" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); max-width: 100%; height: 30px; display: inline; vertical-align: -14px; line-height: inherit; max-height: 31.25rem; width: 17px;"> $ ,

$a 2 " class="formula-container wants-props-update" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); line-height: inherit; display: inline-block;"> a 2 " class="Wirisformula" role="img" alt="a subscript 2" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); max-width: 100%; height: 30px; display: inline; vertical-align: -14px; line-height: inherit; max-height: 31.25rem; width: 17px;"> $ ,

$a 3 " class="formula-container wants-props-update" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); line-height: inherit; display: inline-block;"> a 3 " class="Wirisformula" role="img" alt="a subscript 3" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); max-width: 100%; height: 30px; display: inline; vertical-align: -14px; line-height: inherit; max-height: 31.25rem; width: 17px;"> $

can assume to be 1.

Submit .py or .zip file.

Please put all of your files into a directory and compress them into a compressed file (.zip, .rar will be accepted).

assignment1-1s2ibujt.png

Anubhav · Accepted Answer

Jacobian matrix for 3 prismatic joint in the assignment problem:-
Expanding the rotation matrix of  we get
			
					
Hence	 
That implies	
Let this be equation 1
				
	The above equation reduces to 
	
	Hence,

1) All prismatic manipulator is a simple manipulator. You can read its Jacobian matrix by inspecting the coordinates. Please derivate the Inverse Jacobian Matrix for this manipulator, write them down...

Answer To: 1) All prismatic manipulator is a simple manipulator. You can read its Jacobian matrix by inspecting...

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