Most CAD modelers do have some basic rendering and animation tools. However, most animation products are far superior for creating motion and rendering out the results.
I happen to use Softimage XSI, but Maya, 3D Studio and Lightwave could certainly perform similar mechanical animation results.
The biggest issue is having skills with one of these programs. Although, a lot of mechical movement could be done without knowing a lot of the product. If you don't have much time to invest, it might be best to create your animations in the native CAD product you are using.
Fundamentally, any animation you create is going to be made as a series of still images. The next step in the process is to take the still images and compress them into a video file such as an .avi, .mov, .mpg and many others. So you will need to look into video editing software. Adobe Premiere is very common.
The exception to this, is if you are trying to create a Flash vector animation. Then instead of producing a series of still images, you would create a Flash vector movie. This is ideal if you want just the outline of shapes with solid colors. To make Flash movies directly from your animation product you will need a seperate product for this.
Any of the products I have named have 30 day trials.
Hope this helps,
Ohmanoggin