This paper describes a new piecewise rotational transformation model for capturing the articulation of joints such as the hip and the knee. While a simple piecewise rigid model can be applied, such models suffer from discontinuities at the motion boundary leading to both folding and stretching. Our model avoids both of these problems by constructing a provably continuous transformation along the motion interface. We embed this transformation model within the robust point matching framework and demonstrate its successful application to both synthetic data, and to serial x-ray CT mouse images. In the later case, our model captures the articulation of six joints, namely the left/right hip, the left/right knee and the left/right ankle. In the future such a model could be used to initialize non-rigid registrations of images from different subjects, as well as, be embedded in intensity-based and integrated registration algorithms. It could also be applied to human data in cases where articulated motion is an issue (e.g. image guided prostate radiotherapy, lower extremity CT angiography).