I'm not sure how to word this question correctly, so I'm going to provide some pictures first off to help visualize this.

Here are some views of what I'm creating:  http://imgur.com/gallery/un9dX 

Ok so basically I am trying to create some spokes that are extruding out of the cylinder in the middle.

Here's what I tried, in picture form first: http://imgur.com/gallery/683FN

As you can see, I made a sketch of the spokes, and then extruded them to the next surface. All is fine, except for the glaring fact that the spokes are extruding out of the body, and I don't want that!! I tried cutting the extrusions out, but it just left some unsightly holes that ruin the whole design.

Please help me with this problem! I can provide anything needed to help, such as the solidworks file or pictures of the real world object.

Sorry if I missed anything that I should've included in the post, I am new here.