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According to the demand of multi-dimensional motion simulation, a class of planar underactuated simulator with cylindrical helical springs was put forward. The workspace of the proposed simulator was restricted by the axial and lateral stiffness of cylindrical helical spring, and 3-DOF of the proposed simulator was driven by only two drive limbs and dynamic coupling effects. The cylindrical helical springs could be seen as an elastic limb Re/Pe/Re, so the simulator can be transformed to an elastic underactuated mechanism, 2RPR/2Re/Pe/Re. The input selection of equivalent mechanism was analyzed by using Grassmann geometry. Based on screws, the kinematics of equivalent mechanism was given. The kinematics can be represented to any frame easily by using the shifting property of the screws. Referring to the influence coefficient and virtual work principles, the statics analysis was performed, and the statics constraint equation was gotten. Finally, the continuous nonlinear compliance model of the mechanism was established, and based on this, the direction stiffness was given.