This chapter is dedicated to the position analysis of mechanisms. Both closed-form and numerical solutions are presented. Position analysis is the most fundamental type of kinematic analyses. Once position of a point or orientation of a rigid body is obtained as a function of time, finding velocity or acceleration functions would be easy; as they just need differentiation of the position function with respect to time. One way for performing position analysis is to use the vector-loop method. This method results in simultaneous nonlinear equations that have multiple solutions.