A New Approach to Generating Ruled Surfaces with Rigid Body Motion

In this paper, we introduce a new method for building ruled surfaces using dual quaternion curves and straight lines. We proved that the rigid body motion, arranged from any straight line in Euclidean 3-space and any dual quaternion curve, produces a ruled surface in Euclidean 3-space when the parameter of the straight line is different from the parameter of the dual quaternion curve. We show that the ruled surface can be expressed by two separate rigid transformations. Moreover, we show that if the rotation part of the dual quaternion curve is a constant unit real quaternion, then the rigid body motion creates a developable ruled surface in Euclidean 3-space. We show that this developable ruled surface also represents a generalized cylinder.