The Simulation Algorithm in Five Steps

Like the dynamic simulation algorithm fw a single closed chain, the algorithm developed here for simple closed-chain mechanisms may also be presented as a series of steps. In this case, five computational steps are required, and they are as follows  

The fundamental computations required in each of these steps are summarized in Table 6.1. 

In Stq 1, the Direct Dynamics problem is solved for each chain of the mechanism assuming that the reference memba has beoi removed and each chain is in an open, unconstrained state. The general open-chain acceleration veclws, (4t)open and (itk)open, are computed fw each chain, along with the position-dependent matrices, ilk and Aj . 

In Step 2, Equation 6.38 is used to find an explicit solution for ao, the spatial acceleration of the reforace member, via linear system solution. The quantities (Mt St) and [Mt X ], required fw both Pt and Rt, are computed in the determination of the explicit relationship between h and ao. This relationship is found by linear system solution using Equation 6.29, with the solution taking the fwm of Equation 6.31, repeated for convenience in Table 6.1. In Step 3, 

Step 5. Integrate to obtain the next state positions and rates for the system. 

---