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This paper presents the direct kinematics solutions for a novel 3-PRS parallel mechanism. The geometric method is applied to formulate three coupled trigonometric equations. One algorithm for solving the three coupled equations is to use the Bezout’s elimination method which leads to a total of 64 solutions. By categorizing the 64 solutions into six groups and further examining the corresponding configuration for each group, the preferred solution to the direct kinematics problem can be obtained. The other approach for solving the coupled equations is to apply the optimization techniques with side and behavior constraints set by analyzing undesired configurations. This approach can obtain the preferred solution without checking all the possible solutions. Moreover, it can perform more efficiently than the elimination method. [Copyright &y& Elsevier]