As the energy efficiency is a worldwide topic for sustainability in sustainable manufacturing, the industry ought to undertake the responsibility in a low-energy manner. For energy efficiency, this paper proposed a novel lightweight Non-holonomic Spherical Underactuated Robot (NSUR) with lower energy consumption and fewer actuators than traditional robotics. The kinematics of a robot refers the motion analysis, such as coordinates, velocity, and acceleration. However, current researches always focus on the holonomic full-actuated robot. This paper is devoted to a kind of novel NSUR and its theoretical kinematics analysis model. After NSUR was introduced, the kinematic representation of NSUR was discussed. A pair inverse and forward kinematics analysis of NSUR was put forward in detail. The kinematic analysis of joint of underactuated robot, as the application of NSUR, is applied to explain and verify this methodology. The measurements and comparisons of energy efficiency between NSUR and traditional robotics are also derived in detail.