Nonlinear Analysis of Flexible Parallel Mechanisms Through Bézier-Based Integration

The slider-crank mechanism, a fundamental component in various engineering applications, including automobile engines and pumps, features three revolute joints and one prismatic joint while possessing only one degree of freedom. This chapter comprehensively analyzes this mechanism, considering its components' rigid and flexible behaviors and introducing a newly developed Bézier-based integration approach to solve the governing equation. In this chapter, by extending the Equation of Motion (EOM), innovative methods such as Greenwood, Augmented, Elimination, and Integrated Multiplier are introduced and implemented to convert Differential Algebraic Equations (DAEs) to Ordinary Differential Equations (ODEs). Additionally, implementing Bézier-based integration is proposed as an alternative to conventional approaches like Runge–Kutta methods and Euler due to its potential for significantly reducing execution time without compromising accuracy. Therefore, the primary objective of this chapter is to investigate how adopting Bézier-based integration can revolutionize real-time dynamics simulations of the slider-crank mechanism. It is demonstrated that incorporating Bézier-based integration leads to enhanced computational efficiency without sacrificing precision or reliability during real-time dynamics simulations. This research contributes significant insights into advancing simulation methodologies for complex mechanisms like the slider-crank system. For instance, using the Bézier technique can reduce the elapsed time to 45%.