For describing the spatial motion of a rigid body, we need to be able to determine its position and orientation at every moment. In some applications, the orientation of the body is not precisely defined, hence the need arises for algorithms that automatically determine the "natural" change in the body's orientation along the computed path, aligning the body's principal axes with an orthonormal frame defined at each point. In CAD applications, it is particularly important for the vectors of this frame to be rational functions, meaning that the trajectory of the rigid body's center must be a curve with a Pythagorean hodograph, or simply a PH curve. We will initially introduce the class of polynomial PH curves and a special adapted frame obtained directly from the quaternion representation of PH curves. Then, we will present a scheme for spatial C1 Hermite interpolation with PH cubic biarcs and use it for designing motions with Euler-Rodrigues frame.