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content/zettels/jacobian.md
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title = "Jacobian"
author = ["Dehaeze Thomas"]
draft = false
category = "Control Theory"
subcategory = "Multivariable Analysis"
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## Jacobian Matrices of a Parallel Manipulator {#jacobian-matrices-of-a-parallel-manipulator}
From (<a href="#citeproc_bib_item_1">Taghirad 2013</a>):
From (<a href="#citeproc_bib_item_2">Taghirad 2013</a>):
> The Jacobian matrix not only reveals the **relation between the joint variable velocities of a parallel manipulator to the moving platform linear and angular velocities**, it also constructs the transformation needed to find the **actuator forces from the forces and moments acting on the moving platform**.
(NO_ITEM_DATA:merlet06_jacob_manip_condit_number_accur_paral_robot)
(<a href="#citeproc_bib_item_1">Merlet 2006</a>)
## Computing the Jacobian Matrix {#computing-the-jacobian-matrix}
How to derive the Jacobian matrix is well explained in chapter 4 of (<a href="#citeproc_bib_item_1">Taghirad 2013</a>) ([notes]({{< relref "taghirad13_paral.md" >}})).
How to derive the Jacobian matrix is well explained in chapter 4 of (<a href="#citeproc_bib_item_2">Taghirad 2013</a>) ([notes]({{< relref "taghirad13_paral.md" >}})).
Consider parallel manipulator shown in [Figure 1](#figure--fig:jacobian-geometry) (it represents a Stewart platform).
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## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Taghirad, H. 2013. <i>Parallel Robots : Mechanics and Control</i>. Boca Raton, FL: CRC Press.</div>
<div class="csl-entry">NO_ITEM_DATA:merlet06_jacob_manip_condit_number_accur_paral_robot</div>
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Merlet, J. P. 2006. <i>Parallel Robots</i>. 2nd ed. Springer Publishing Company, Incorporated.</div>
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>Taghirad, H. 2013. <i>Parallel Robots : Mechanics and Control</i>. Boca Raton, FL: CRC Press.</div>
</div>