To do this we will have to give proper constrains and through drive constraint we can animate a pinion on rack. File used in the tutorial is hosted on the link below:-
After creating a new assembly file and saving it first we will place the penion part. Because it is grounded and we want to re-constrain it, remove its grounded position. Very first we will mate the pinion's axis to the X axis of the assembly then we will mate the assembly's origin centre point to the pinion's origin center point. Now the pinion is moving only on the axis displayed. That is all for pinion part for now.
Now we will place the rack in the assembly. We will give tangent mate as displayed in the video. Select the outside solution. Afterward we will give 0 degree angle mate the assembly's XZ plane and Rack's XZ plane. Now we will mate Penion's Top plane to Rack's (User Defined) Work Plane 7. Now suppress this mate because rack has moved to the place which we require. Now we will give 0 degree angle mate to assembly' XY plane and Pinion's Top plane. Now we will give Rotation-Translation constrain between Rack and Pinion. First select the part rotates here it is pinion and then the rack it is important. In the distance specify 4.725 units. Now drive constraint the angle mate 2 constrain as described in the video if it is moving in other direction fill -360 degree or moving very fast fill less amount in Increment tab. When you will give the mate and it does not look like in video then try flush mate to get desired result. That is all.
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