It is shown how the independent loops inherent in kinematic chains with multidegrees of freedom are utilized to set up and solve the governing kinematic equations for displacement, velocity, and acceleration. The need to solve systems of nonlinear algebraic (displacement) equations is bypassed by formulating the problem as a system of nonlinear differential equations. In a numerical example, it is shown in detail how the method is applied and a Stirling cycle engine is kinematically analyzed for less than one dollar of computer time. The significance of possible singular configurations in a mechanism is discussed and stratagems are given for handling special cases.

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