FILL-IN-THE-BLANK: We need pure rotations and translations to characterize the ______________ and orientation of a point relative to the coordinate frame attached to the base.

(a). Explain briefly what problem we face when try to use composition of geometrical transformations including translation. (b). Describe homogeneous coordinates. Demonstrate how issue of translation is resolved using homogeneous coordinates. (c). Illustrate use of homogeneous coordinates by giving at least one example from two dimensional and three dimensional geometry with combining transformations; reflection, rotation and translation

orWatch a videoThe point B(–1,–5) is rotated 90° counterclockwise around the origin. What are the coordinates of the resulting point, B'?

A viewer is located at position (2, 3, 5) looking at the car locate at origin (0, 0, 0). Find out the axes orientation with respect to the viewer. Assume the viewer is on the ground.

what would the point 6,4 be after a 90 clockwise rotation

FILL-IN-THE-BLANK: Robot kinematics is basically about looking at the position, orientation and velocity of the _____________ frame with respect to the base frame.