14.1: Flowchart Preparation
Before starting with the kinematic and kinetic analysis, it is very important to collect all relevant information, simplify it and choose the coordinate systems to analyse the problem along the following steps that are also shown below in the flow-chart preparation:
- Can the problem be segmented in time?
- If yes, then split the problem in segments and analyse each segment separately. The initial conditions of a segment (initial positions and velocities) are determined from the end conditions of the preceding segment.
- Choose one or more coordinate systems (CS) to analyse the kinematics. Use the provided information to choose the system(s) which makes the analysis simplest.
- Make a sketch of the problem that contains all relevant objects, constraints and coordinate systems.
- Write down all variables, given values and other relevant equations and information.
- Determine all degrees of freedom (DOFs) needed to uniquely determine the positions and orientations of all objects. E.g. \(x_{P}, y_{P}\) for every point mass \(P\) and \(x_{G}, y_{G}\) and \(\phi\) for every rigid body.
- Determine the constraint equations and count the number of DOFs.
- Reduce the number of DOF: using constraint equations, e.g. from fixed points, joints, path curves.
- Determine the position vectors \(\overrightarrow{\boldsymbol{r}}\) and components of all relevant points using the CS.
- Determine if a kinematic or kinetic analysis is needed. If there is enough information to solve the problem without considering the effect of forces the problem can be solved with kinematics (go to step 11). Otherwise, first the effect of forces should be determined using kinetics (go to step 18) and then the EoM is solved.