The hierarchical model that you created is controlled by forward kinematics; that is, the positions of the parts vary as a function of joint angles. More mathematically stated, the positions of the joints are computed as a function of the degrees of freedom (these DOFs are most often rotations). The problem of inverse kinematics is to determine the DOFs of a model to satisfy a set of positional constraints, subject to the DOF constraints of the model (a knee on a human model, for instance, should not bend backwards).
This is a significantly harder problem than forward kinematics. Aside from the complicated math involved, many inverse kinematics problems do not have unique solutions. Imagine a human model, with the feet constrained to the ground. Now we wish to place the hand, say, about five feet off the ground. We need to figure out the value of every joint angle in the body to achieve the desired pose. Clearly, there are an infinite number of solutions. Which one is "best"?
Now imagine that we wish to place the hand 15 feet off the ground. It's fairly unlikely that a realistic human model can do this with its feet still planted on the ground. But inverse kinematics must provide a good solution anyway. How is a good solution defined?
Your solver should be fully general and not rely on your specific model (although you can assume that the degrees of freedom are all rotational). Additionally, you should modify your user interface to allow interactive control of your model though the inverse kinematics solver. The solver should run quickly enough to respond to mouse movement.
If you're interested in implementing this, you will probably want to consult the CSE558 lecture notes.
The primitives that you are using in your model are all built from simple two dimensional polygons. That's how most everything is handled in the OpenGL graphics world. Everything ends up getting reduced to triangles.
Building a highly detailed polygonal model often requires millions of triangles. This can be a huge burden on the graphics hardware. One approach to alleviating this problem is to draw the model using varying levels of detail. In the modeler application, this can be done by specifying the quality (poor, low, medium, high). This unfortunately is a fairly hacky solution to a more general problem.
First, implement a method for controlling the level of detail of an arbitrary polygonal model. You will probably want to devise some way of representing the model in a file. Ideally, you should not need to load the entire file into memory if you're drawing a low-detail representation.
Now the question arises: how much detail do we need to make a visually nice image? This depends on a lot of factors. Farther objects can be drawn with fewer polygons, since they're smaller on screen. See Hugues Hoppe's work on View-dependent refinement of progressive meshes for some cool demos of this. Implement this or a similar method, making sure that your user interface supplies enough information to demonstrate the benefits of using your method. There are many other criteria to consider that you may want to use, such as lighting and shading (dark objects require less detail than light ones; objects with matte finishes require less detail than shiny objects).
Many 3D models come in the form of static polygon meshes. That is, all the geometry is there, but there is no inherent hierarchy. These models may come from various sources, for instance 3D scans. Implement a system to easily give the model some sort of hierarchical structure. This may be through the user interface, or perhaps by fitting an model with a known hierarchical structure to the polygon mesh (see this for one way you might do this). If you choose to have a manual user interface, it should be very intuitive.
Through your implementation, you should be able to specify how the deformations at the joints should be done. On a model of a human, for instance, a bending elbow should result in the appropriate deformation of the mesh around the elbow (and, if you're really ambitious, some bulging in the biceps).