This paper introduces a novel compact three-degree-of-freedom (DOF) parallel robot that will be used as a leg of a 9-DOF kinematically redundant parallel robot. First, the kinematic model of the robot is established based on geometric constraint conditions. Then, the inverse and forward kinematic problems are solved. The inverse problem is straightforward, while the forward problem can be solved analytically by three different approaches. Afterward, a singularity analysis is presented based on the Jacobian matrices derived from the kinematic model. The mathematical conditions for singularities are obtained and their geometric interpretation is given. Finally, the workspace of the robot is analyzed and is shown to correspond to a portion of a torus. The analysis reveals that the robot can have a singularity-free workspace of significant size relative to its footprint provided that some simple limitations are introduced at the design stage.