A Numerical Integration Algorithm Based on the Introduction of a Constraint Violation Factor
The direct dynamic solution approach developed here for closed-chain mechanisms is based on Lagrangian formalism, relative coordinates and constraint equations derived from loop-closure conditions. In this way, the dynamical problem is formulated as a system of Lagrange differential equations in the relative coordinates, accompanied by second-order constraints, these equations are linear in the second-order terms and are solved by a numerical integration procedure. Integration algorithms determine numerical stability and global features of direct dynamic analysis in a large extent.
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