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The ParkourBot climbs in a planar reduced-gravity vertical chute by leaping back and forth between the chute's two parallel walls. The ParkourBot is comprised of a body with two springy legs and its controls consist of leg angles at touchdown and the energy stored in them. During flight, the robot stores elastic potential energy in its springy legs and then converts this potential energy in to kinetic energy at touchdown, when it “kicks off” a wall. This paper describes the ParkourBot's mechanical design, modeling, and open-loop climbing experiments. The mechanical design makes use of the BowLeg, previously used for hopping on a flat ground. We introduce two models of the BowLeg ParkourBot: one is based on a nonzero stance duration using the spring-loaded inverted pendulum model, and the other is a simplified model (the simplest parkour model, or SPM) obtained as the leg stiffness approaches infinity and the stance time approaches zero. The SPM approximation provides the advantage of closed-form calculations. Finally, predictions of the models are validated by experiments in open-loop climbing in a reduced-gravity planar environment provided by an air table.