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Subsections

dTdqi

Syntax

void dTdqi(Matrix & dRot, ColumnVector & dp, const int i);
ReturnMatrix dTdqi(const int i);

Description

This function computes the partial derivatives:
$\displaystyle \frac{\partial {}^0 \mbox{\boldmath$ T $}_n}{\partial q_i}$ $\textstyle =$ $\displaystyle {}^0 \mbox{\boldmath$ T $}_{i-1} \mbox{\boldmath$ Q $}_i \; {}^{i-1} \mbox{\boldmath$ T $}_n$ (2.62)

in standard notation and
$\displaystyle \frac{\partial {}^0 \mbox{\boldmath$ T $}_n}{\partial q_i}$ $\textstyle =$ $\displaystyle {}^0 \mbox{\boldmath$ T $}_{i} \mbox{\boldmath$ Q $}_i \; {}^{i} \mbox{\boldmath$ T $}_n$ (2.63)

in modified notation, with
$\displaystyle \mbox{\boldmath$ Q $}_i$ $\textstyle =$ $\displaystyle \left[\begin{array}{cccc}
0 & -1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \end{array}\right] \mbox{ for a revolute joint}$ (2.64)
$\displaystyle \mbox{\boldmath$ Q $}_i$ $\textstyle =$ $\displaystyle \left[\begin{array}{cccc}
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0 \end{array}\right] \mbox{ for a prismatic joint}$ (2.65)

Return Value

Matrix or None (in this case dRot and dp are modified on output)



Richard Gourdeau 2004-07-06