**A closer look at ****motion analysis**

**Paul Kurowski**

*President*

Design Generator Inc.

London, Ontario, Canada

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.

### WHAT'S THE DIFFERENCE BETWEEN VIBRATION AND DYNAMIC ANALYSES?

Vibration analysis examines the motion of a structure that involves deformations (usually elastic) about a point of equilibrium.

Dynamic analysis is a more general term that encompasses any analysis considering the inertial effects. It can be the analysis of a structure, a mechanism, or a rigid or elastic mechanism component. The objective of a dynamic analysis may be to find data of interest, such as velocities, accelerations, inertial loads, deformations, stresses, and natural frequencies. Either motion analysis, FEA, or both, are used depending on the analyzed problem.

### Rigid-body motion

A ball joint has three rigid-body motions meaning it can move in three independent directions (three rotations) without deformation. Therefore, three independent variables (or three degrees of freedom) are required to describe the position of this mechanism.

A plate siding on another plate also has three rigid-body motions. It can slide in two directions (X and *Y*) and rotate (about the *Z *axis ) in one direction without deforming. Three independent variables are required to describe position of this mechanism.

A four-bar linkage has one rigid-body motion. One independent variable (an angular position of any link) is required to describe the position of this mechanism.

Note that all these mechanisms also have degrees of freedom due to motion resulting from elastic deformations. These are sometimes called elastic modes and are related to modes of vibration.

Statements such as "this mechanism has one rigid body motion" does not mean its components do not deform under load. It means that motion can take place without component deformations. The terms rigid-body mode or rigid-body movement are used alternately to rigid-body motion.

## A QUICK COMPARISON OF FEA AND MOTION ANALYSIS | ||

CAN ANALYZE | FEA | MOTION |

Structures | Yes | No |

Mechanisms | No | Yes |

Deformations and stresses | Yes | No |

Vibration | Yes | No |

Models with rigid body motions | No* | Yes |

Models with meshes | Yes | No |

Models prepared in CAD | Yes | Yes |

* Using special techniques FEA can handle modal analysis with rigid body motions | ||

Motion -analysis software can analyze vibration when a model includes elastic components. And special modeling techniques such as adding soft springs or inertial relief to a model can eliminate rigid-body motions. In effect, structures with rigid-body motions can be analyzed with FEA. However, the model is still treated as a structure and not as a mechanism. |

### Common types of vibration analyses

All these types of vibration analyses belong to the family of structural analysis and are performed with FEA.

**MODAL ANALYSIS **finds natural frequencies and the associated shapes of vibration.

**DYNAMIC TIME ****ANALYSIS **calculates vibrations caused by loads with explicitly known time histories.

**DYNAMIC FREQUENCY ****ANALYSIS **most often denotes an analysis of steady-state vibration due to harmonic excitation.

**DYNAMIC RANDOM **vibration analysis simulates vibrations from random excitations