A new type of parallel robot mechanism with an extendable structure is presented, and its kinematic properties and design parameters are analyzed. The Triple Scissor Extender (TSE) is a 6 Degree-Of-Freedom robotic mechanism for reaching high ceilings and positioning an end effector. Three scissor mechanisms are arranged in parallel, with the bottom ends coupled to linear slides, and the top vertex attached to an end effector plate. Arbitrary positions and orientations of the end effector can be achieved through the coordinated motion of the six linear actuators located at the base. By changing key geometric parameters, the TSE's design can yield a specific desired workspace volume and differential motion behavior. A general kinematic model for diverse TSEs is derived, and the kinematic properties, including workspace, singularity, and the Jacobian singular values, are evaluated. From these expressions, four key design parameters are identified, and their sensitivity upon the workspace volume and the Jacobian singular values is analyzed. A case study in autonomous aircraft assembly is presented using the insights gained from the design parameter studies.