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In this paper, we propose the design of a planar biped for which the model is nearly linear, i.e., the inertia matrix is a constant and the gravity terms in the equations of motion are still nonlinear, but simplified. The legs are designed such that the inertia matrix is independent of the joint variables. As a result, the nonlinear terms in the centrifugal and Coriolis terms disappear. In this design, each leg has two links that are connected by a revolute joint at the knee. The two legs are connected to each other at the hip. The center of mass of each leg is located at the hip, using counterweights. We assume that the stance leg is locked at the knee during the support phase. For this system, dynamic model for complete walking, i.e., swing phase, knee lock, and foot impact are considered. Motion control for trajectory following of this design is studied using a nonlinear controller. The paper discusses the issue of tracking of desired trajectories during the full cycle motion.