In this paper, possibilities for workspace enlargement and joint trajectory optimization of a (6 + 3)-degree-of-freedom kinematically redundant hybrid parallel robot are investigated. The inverse kinematic problem of the robot can be solved analytically, which is a desirable property of redundant robots, and is implemented in the investigations. A new method for detecting mechanical interferences between two links which are not directly connected is proposed for evaluating the workspace. Redundant degrees-of-freedom are optimized in order to further expand the workspace. An approach for determining the desired redundant joint coordinates is developed so that a performance index can be minimized approximately when the robot is following a prescribed Cartesian trajectory. The presented approaches are readily applicable to other kinematically redundant hybrid parallel robots proposed by the authors.