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Пишет друг друга пердуна (![[info]](http://lj.rossia.org/img/userinfo.gif){kind=small} oort)@ 2024-03-03 01:39:00 |
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Topology and the robot arm
https://www.math.purdue.edu/~gottlieb/B
A robot arm is in effect a smooth function from the space of positions of the arm to the space of positions of a coordinate frame attached to the end of the arm. For the most common robots built today, this means a map f: T^n \to R^3 \times SO_3. We describe the singularities of this map. The set of rotational singularities is the set of arm positions where the axes of the links are parallel to a plane. Thus, it is always two-dimensional. Also, we show that f is homotopic to a map which factors through a circle, and represents the generator of pi_1(SO_3). The engineering implication of these statements are discussed.
https://www.math.purdue.edu/~gottlieb/B
A robot arm is in effect a smooth function from the space of positions of the arm to the space of positions of a coordinate frame attached to the end of the arm. For the most common robots built today, this means a map f: T^n \to R^3 \times SO_3. We describe the singularities of this map. The set of rotational singularities is the set of arm positions where the axes of the links are parallel to a plane. Thus, it is always two-dimensional. Also, we show that f is homotopic to a map which factors through a circle, and represents the generator of pi_1(SO_3). The engineering implication of these statements are discussed.
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