In this paper five different optimization strategies for kinematically redundant mechanisms, i.e. mechanisms having additional actuator(s) in at least one kinematic chain, are presented. They are based on two main approaches, a discrete optimization and a classical continuous optimization. Exemplarily, a planar, kinematically redundant 3RRR-based mechanism is introduced. The position of its redundant actuator, i.e. the robot geometry, is optimized according to an optimization criterion that is denoted as the gain of the maximal homogenized pose error. Several analysis examples demonstrate the effectiveness of kinematic redundancy with respect to the introduced optimization procedures. It is shown that in comparison to discrete approaches, classical continuousbased optimization strategies do not necessarily lead to more appropriate results in terms of performance improvement.