Abstract-- We present a novel general model that unifies the kinematics of constant curvature and constant twist continuum manipulators. Combining this kinematics with energy-based physics, we derive a linear mapping from actuator configuration to manipulator deformation that is analogous to traditional robot forward kinematics. The combination of generality and linearity makes the model useful for control and planning algorithms. Finally, our model is shown to be accurate through experimental validation on manipulators with pneumatic artificial muscles. I. INTRODUCTION While the motion of traditional robots comes from their discrete joints, a continuum manipulator moves by deforming along its entire arc. These manipulators are often composed of rigid skeletons and soft actuators.