A parallel robot or parallel kinematics mechanism is provided for uses such as robotics or machining. The mechanism comprises a fixed base, a main arm, and a first and second support arm to position and orient an object in a cylindrical space with at least three degrees of freedom and retained inclination. The main arm includes an end component for supporting the object and linkage means to retain the inclination of the end component with respect to the base for all positions and orientations of the end component. The mechanism advantageously provides a large cylindrical workspace and a small footprint and is capable of moving an object at high accelerations and speeds. The mechanism can be equipped with an additional motor to orient an object, thereby providing the mobility of a SCARA robot. Alternatively, it can be equipped with passive transmission means that allow for an object to be displaced in parallel to itself.