How to calculate torque due to gravity of a 3D linkage mechanism? I am performing a static analysis of a Baxter Robot arm. How to calculate the torques at each of the joints ?
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could you please provide context to your question... – ZeroTheHero Mar 18 '17 at 21:34
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I am performing a static analysis of a Baxter Robot arm. How to calculate the torques at each of the joints ? – Riddhi Mar 18 '17 at 21:54
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You should think of including a diagram for clarity. – ZeroTheHero Mar 18 '17 at 22:03
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What are the forces (magnitude, direction, point of application)? Do you know to calculate the torque due to one force? – sammy gerbil Mar 18 '17 at 22:42
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I only need to calculate the torque due to gravity. The mass of all the links are known. – Riddhi Mar 18 '17 at 22:46
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Find the total mass $m$ and the center of mass vector $\mathbf{c}$ of all the arms above the motor and use the following equipollent forces and moments to find the reactions.
$$ \begin{align} \mathbf{F} & = m \mathbf{g} \\ \mathbf{M} & = \mathbf{c} \times m \mathbf{g} \end{align} $$ where $\mathbf{g}$ is the acceleration of gravity vector.
Now if the motor joint is along the $\mathbf{z}$ direction and located at $\mathbf{r}$ then to obey the static condition to motor torque $\tau$ has to counter act the moment along the joint axis, or
$$\mathbf{z} \cdot \mathbf{M} + (\mathbf{r} \times \mathbf{z}) \cdot \mathbf{F} = \tau$$
where $\cdot$ is the vector dot product.
John Alexiou
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