Take you big mounting board. Make a wall surrounding the board. make sure the board can move back and forth.Make sure that you have smooth bricks to ensure that the board can move very freely. Don't worry about the paper and the motor yet.
Now we will attach the motor. take you tethered dc motor and attach the wheel. Place the motor on a small mounting board. To secure the motor, you first want to build up two poles of legos. Then put in supporting bricks in the middle of the motor. finally, attach a cross beam to secure the motor in place. IMPORTANT: make sure the motor is flush to the board. (I'm using a servo motor in examples, use a dc in yours. I also built the example so low that I didn't need middle supporting bricks.)
Congrats! you have finished 25% of the project! Now, build two columns. then make a supporting beam across the like a bridge. Don't worry about the strings or the motor yet. Then place 1 by 2s and smooth bricks to act like a "rail" for the next big part.
Now you will have to build the moving part that will hold the syringe. This is one of the hardest parts. In order to build the rail, you have to make it: larger then the syringe, a good system so the piece won't fall out, be able to actually hold the syringe, and a spot the motor will be to move the piece.
Almost there! now, build a sturdy tower to hold your second motor. Like what we did with the bottom motor, attach the small mounting board to the motor and also attach the wheel. Place the motor in the tower you should of made. The tower should be around the middle of the bridge. IMPORTANT: make sure the wheel is flush to your moving piece.
You are 99% done! all you have to do is to attach the syringe to your moving piece. I know what your thinking, what are all of the strings and paper for? Well, the strings held my syringe because a rubber band couldn't do the job. The paper scraps were to get the motors exactly flush to the piece.