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In this work, we present a simple framework to synthesize human motion. Our main goal is to propose a methodology tailored for inexperienced users to initiate their research in human motion simulation and human motion trajectory optimization. The novelties of the work include the following. First, trigonometric splines are used instead of traditional B-splines to discretize the generalized coordinates and velocities. Second, useful identities for trigonometric splines are derived. Third, this work is intended to be an example, so that even non-skilled users, such as undergraduate students, can perform human motion analysis using a high-level programming language such as MATLAB. Four simulations of human motion are generated: walking, sitting and standing, side-step, and jump. The results of the walking simulation are validated by experiments. Simulation and experimental results are presented and discussed.