ch10oddslns

# ch10oddslns - Angel Interactive Computer Graphics Fifth...

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Angel: Interactive Computer Graphics; Fifth Edition Chapter 10 Solutions 10.1 If the upper arm is longer than the lower arm then, as a Frst approximation, the robot can reach all points within a sphere centered at the joint on the base. However, this answer is only approximate because the lower arm cannot move below the level of the base, so a second approximation is a hemisphere above the base. This approximation has to have added to it points below the base that can be reached by the lower arm while the upper arm is parallel to the top of the base, a set of points that depends on the length of the upper arm and the radius of the base. If the lower arm is longer than the upper arm, then there will be an interior sphere radius equal to the di±erence in the arm lengths that cannot be reached. 10.3 ²or this simple example, there are three values of the joint angles and three coordinates in space, so there are a couple of simple approaches that can work. One is to usethe result in the previous problem to solve for the

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ch10oddslns - Angel Interactive Computer Graphics Fifth...

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