There is not any tool for extracting object’s motion trail to curve. But this problem can be solved by simple MEL script.

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$obj = "box01";  // user object

float $pos[3] = `getAttr($obj+".translate")`;

string $curveName = `curve -ws -p $pos[0] $pos[1] $pos[2]`;

$currTime = `currentTime -q`;

for ($i=2; $i<200; $i++)

{

currentTime -edit $i;

$pos = `getAttr($obj+".translate")`;

curve -append -p $pos[0] $pos[1] $pos[2] $curveName;

}
Object motion trail to curve
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