In short, yes it is possible to gain some muscle using only machines and no free weights.  Adding size to the major muscle groups like your arms, shoulders and legs is usually not a problem for someone who only has access to a few machines.   Strength training machines are sometimes used more for toning the muscles instead of gaining, but with the right workouts it is possible to still gain muscle.  Use a workout routine that incorporates high weight with fewer repetitions.

You should use the heaviest weight you possibly can to fatigue the muscles and increase that weight over time to keep the muscles stressed.  Start with 3 sets of 6 reps on the machine and if you feel you can do more, either add more weight or keep doing more reps until the muscles feel exhausted.  If you choose to do only more reps, you should add more weight next time so your muscles get a constant challenge.  Free weights are needed if you are looking to gain a lot of muscle but you can use the machines you have access to for as long as you can and you will still see some muscle gain.  Add whey protein to your diet and increase how many calories you consume to help the muscles grow.