A closer look at motion analysis

A closer look at motion analysis

Paul Kurowski
President
Design Generator Inc.
London, Ontario, Canada

Many industries in the last decade successfully implemented finite-element analysis as a tool for product development. The success of FEA is now being followed by more widely used motion-analysis software. These two numerical tools are often used together to put new designs through their paces, rather than doing almost the same with costly physical prototypes.

But the wider use of motion analysis along with FEA clouds the capabilities and limitations of each tool. To clear up the confusion, it's useful to examine the role of both, describe their range of applications, and explain how these two tools work together.

A CLOSER LOOK
Let's start with FEA, a tool for structural analysis. A structure is basically an object with a firm support. Note that firmly supported objects can still move a bit under load because loads cause deformations. However, the movement can only take the form of vibration about a point of equilibrium. That differentiates FEA into static and dynamic types. Static FEA ignores inertial effects from movement under load. It deals only with deformations and stresses while slowly applying a load.

Analyzing structures subjected to fast changing loads must account for inertial and damping effects. This requires dynamic FEA, or to use a more precise term, vibration FEA. Many types of vibration FEA have been developed to study structural behavior under different types of loading. They all belong to the family of structural analysis and all are performed with FEA, not with motion-analysis tools.

Can FEA also analyze mechanisms? Not ones that move and, of course, stationary mechanisms are more structure than mechanism. FEA cannot analyze mechanisms because a mechanism can move without components experiencing deformation. Mechanism components move as rigid bodies and this is something FEA cannot handle, except for some special cases. The tool to use is motion-analysis software.

What sets motion analysis and FEA further apart is that because motion analysis assumes mechanical components are rigid, deformations and stresses of mechanism components can not considered. FEA, on the other hand, studies deformable, stationary components (structures) but can not touch anything with rigid-body motion.

In some special cases an object can be treated either as a structure or mechanism. Consider the device in A single degree of freedom oscillator. It can be viewed as a structure where mass and stiffness are separated. It has no rigid body motion because mass oscillations require spring deformations. The oscillator can also be seen as a mechanism with rigid link (mass) connected to a ground link by a flexible link (spring). For motion analysis this is a single degree of freedom system in which the rigid link moves along the guide rails. Motion analysis will, therefore, find only one mode of vibration, as should be the case for the single-degree-of-freedom oscillator. However, using FEA we may also find higher modes because FEA considers components as elastic, not rigid as in motion analysis.

These two tools of numerical analysis can work together even though they are quite different. Motion-analysis software works with CAD assemblies rather than single parts because one part is not a mechanism. Motion analysis starts by translating assembly mating conditions into corresponding kinematic pairs such as pin joints, ball joints, and sliders. Motion-analysis software then calculates data of interest such as displacements, velocities, accelerations, joint reactions, and inertial loads within a required range of mechanism motion. Each component, if viewed separately, is under a balanced set of loads (joint reactions and inertial forces) and so the FEA "thinks" the mechanism component is a structure when it's isolated from assembly. In short, motion analysis feeds FEA with data necessary to convert mechanism component into a structure — a form digestible to FEA.

All this is usually done in a matter of seconds, or minutes for complex mechanisms. The same calculations would require hours or days if performed by hand. It's a great exercise for engineering students, but impractical in any industrial application.

Consider a simple example: Find deformations and stresses in the curved link of the quick-return mechanism on the first page. The required procedure can be presented in three steps.

Step 1: Motion analysis determines joint reactions and inertial forces acting on the links of the mechanisms in the specified range of motion. All links are treated as rigid bodies.

Step 2: Loads found in Step 1 are transferred from the assembly to the component (the curved link) selected for analysis. The loads consist of joint reactions and inertial forces. By definition they are in balance. The link, isolated from the mechanism assembly, can now be treated as a structure because it is subjected to a balanced set of loads.

Step 3: FEA can now work on the link to find its deformations and stresses just as if it was a structure.

Motion analysis should not be confused with assembly animation. While animation shows assembly components moving, motion analysis provides complete quantitative information on kinematics (position, velocity, acceleration) and dynamics (forces, moments) of the moving mechanism.

CAD geometry is the starting point for motion analysis and FEA. Therefore, both of these are easiest to use when they run as add-ins to CAD. The common CAD interface enables a comprehensive mechanism analysis early in the product development when designs are still in easy to change electronic format.

The quick-return mechanism shows how FEA and motion analysis mix. The mechanism has one rigid-body motion, so its position is fully defined by, for example, the angular position of the driving link.

These mechanisms move while their components behave as rigid links. Most mechanisms have only one rigid-body motion (one degree of freedom) meaning only one independent variable defines mechanism positions. Some have more rigid-body motions. The industrial robot, for example, has four rigid-body motions. The models were made and analyzed in SolidWorks and its addins CosmosMotion and CosmosWorks.

The first mode of vibration (left) is shown with the undeformed shape overlaid on the deformed shape.

Motion analysis finds joint reactions and inertial forces acting on the curved link (Step 1) selected for stress analysis. Loads found in Step 1 are exported from motion analysis performed on the assembly, to FEA performed on a part (Step 2) so deformation and stress analysis of the link could be conducted (Step 3).

Product design uses CAD, motion analysis, and FEA for virtual testing of the new product and helps eliminating multiple prototyping iterations. Results from motion analysis and FEA can then guide design decisions.

A QUICK COMPARISON OF FEA AND MOTION ANALYSIS