The simulation of mechanical systems often requires modeling of systems of other physical nature, such as hydraulics. In such systems, the numerical stiffness introduced by the hydraulics can become a significant aspect to consider in the modeling, as it can negatively effect to the computational efficiency. The hydraulic system can be described by using the lumped fluid theory. In this approach, a pressure can be integrated from a differential equation in which effective bulk modulus is divided by a volume size. This representation can lead to numerical stiffness as a consequence of which time integration of a hydraulically driven system becomes cumbersome. In this regard, the used multibody formulation plays an important role, as there are many different procedures for the constraint enforcement and different sets of coordinates to choose from. This paper introduces the double-step semirecursive approach and compares it with a penalty-based semirecursive approach in case of coupled multibody and hydraulic dynamics within the monolithic framework. To this end, hydraulically actuated four-bar and quick-return mechanisms are analyzed as case studies. The two approaches are compared in terms of the work cycle, energy balance, constraint violation, and numerical efficiency of the mechanisms. It is concluded that the penalty-based semirecursive approach has a number of advantages compared with the double-step semirecursive approach, which is in accordance with the literature.

机械系统的仿真通常需要对其他物理性质的系统（例如液压系统）进行建模。在这样的系统中，液压系统引入的数值刚度可能会成为建模中要考虑的重要方面，因为它会对计算效率产生负面影响。可以使用集总流体理论来描述液压系统。在这种方法中，可以从微分方程积分压力，其中有效体积模量除以体积大小。这种表示可能导致数值刚度，其结果是液压驱动系统的时间积分变得麻烦。在这方面，所使用的多体公式起着重要作用，因为约束执行有许多不同的过程，并且可以选择不同的坐标集。本文介绍了双步半递归方法，并将其与基于惩罚的半递归方法进行了比较，以解决整体框架内多体和水力学耦合的情况。为此，将对液压驱动的四杆和快速返回机构进行案例分析。比较了这两种方法的工作周期，能量平衡，约束违反和机制的数值效率。得出的结论是，与基于文献的双步半递归方法相比，基于惩罚的半递归方法具有许多优点。作为案例研究分析了液压驱动的四杆和快速返回机构。比较了这两种方法的工作周期，能量平衡，约束违反和机制的数值效率。得出的结论是，与基于文献的双步半递归方法相比，基于惩罚的半递归方法具有许多优势。作为案例研究分析了液压驱动的四杆和快速返回机构。比较了这两种方法的工作周期，能量平衡，约束违反和机制的数值效率。得出的结论是，与基于文献的双步半递归方法相比，基于惩罚的半递归方法具有许多优势。