There is no question that calisthenics can produce incredible upper body strength with impressive muscular development. The lower body is a different story. People are constantly asking if bodyweight training can produce impressive strength and hypertrophy in the legs. My answer? Yes, but not as much as with heavy squats and deads.
Like usual, let me start off with a personal anecdote... I've always had "strong" legs. Back when I lifted, I would squat 1.5x my bodyweight for sets of 10, and deadlift 2x my bodyweight for sets 8 reps. I know that this isn't strong by weightlifting or powerlifting standards, but for a genetically average skinny dude, it isn't too bad. As far as calisthenics go, I have done sets of 20 pistol squats and pretty much always maintain enough leg strength to do a paused "advanced shrimp". I have trained at every end of the spectrum- from "heavy" squats and deads to unweighted squats and hill sprints, and I can assure you that bodyweight training can develop your legs. My observations...
SPRINTS- If you aren't going to lift, hitting the posterior chain in a functional and complete way is best done with sprinting. Find a steep hill and after a thorough warm up, run it hard. For leg development, I prefer a 10-15 second sprint with around a 1-3 minute rest. Depending on the length of the sprint, I will typically aim for 5-10 reps and do this 1-2 times per week. This is the best posterior chain exercise you can do with your bodyweight. Not only will it develop the entire leg, it builds power, athleticism, speed, coordination and a mental toughness.
The Advanced Shrimp- One Of The Hardest Bodyweight Leg Exercises
PISTOLS- This is the go-to leg developer in the calisthenics community. Pistols can strengthen and grow the quads, adductors and glutes. Increasing volume has always been the most effective strategy for me when it comes to training legs. High rep pistols work pretty dang good in this context. 3 sets of 20 reps a few times per week will definitely add some mass to the thighs. If you are into calisthenics, you know that the pistol isn't the only single leg squat. Shrimp squats and variations can be good, but personally I found high rep shrimps to irritate my hip, so I can't speak to their effectiveness as a good exercise for mass, but I see no reason why they wouldn't be. The pistol seems to be a pretty sustainable exercise for most people, but it is pretty high stress, so maintain proper form and don't bounce.
SQUATS AND LUNGES- Pure. Simple. Natural... And seriously underrated. The intensity myth persists- that "the only way to gain muscle is to go heavier and heavier." NOT TRUE. Some of my best leg development has come from doing very high rep squats and lunges as quickly as I could. The burn and pump I would get from these high rep sets was absolutely insane. And, for the first time in my life, I developed a VMO and actual visible vascularity in my quads. I worked up to doing a set of 300 with these almost DAILY, varying the exercise in the following manner- The first day I would do a standard bodyweight squat, the next day I would a hindu squat, and the third day I would do walking lunges. I would just repeat this cycle 6 days per week. My legs didn't get as big as when I was doing barbell squats, but they definitely got more aesthetic.
BAREFOOT RUNNING- I've got some skinny calves. This isn't because I haven't trained them- I literally have tried everything! The only thing that has ever improved them is running, and nothing more so than running barefoot. It took a while to build up to where my achilles tendon could tolerate the stress of running shoeless, but I would run around 10-15 miles per week barefoot or in Vibram 5 fingers. My calves used to by skinny, undefined sticks. Now they are skinny, defined, visibly muscular sticks with a hint of vascularity. I highly recommend running in general. If you have the patience and orthopedic health to do so, barefoot running is an awesome exercise for the lower leg. Just be extraordinarily cautious because most of us have very deconditioned feet and ankles.
STANCE TRAINING AND ISO'S- Yeah these can work too. I come from a traditional martial arts background so stance training was literally the first leg training I ever did. Holding a very low horse stance for increasing amounts of time is a great finisher to do a few times per week. As a side note, I don't practice shrimp squats at all, but I can do the most advanced variation without any specific preparation. I'm certain the reason for this is because of my daily Tai Chi practice. Over the years, I have trained to drop my stances very low during my Tai Chi practice, while controlling all of my transitions and weight shifts. This is pretty much like doing a bunch of slow motion, isometric half-pistols. As far as leg strength goes, proper stance training, especially single leg stance training, can rival single leg squats, but with the added advantage of building strength and control through transitions and weight shifts, which requires a lot of hip strength and stability. It's no joke! The only disadvantage this training has is that even with exceptionally low stances, you rarely go below parallel, which is why I think this type of training transfers better to shrimp squats than pistols.
I'm betting the real question you have is how my leg size compared between weight training and calisthenics. By the tape, my legs were bigger when I was weight training, but I was also around 15-16% bodyfat. My thighs are two to three inches smaller in diameter now, but I'm usually around 12.5% body fat (and getting leaner). Body fat does make a difference, but I'm not under any illusion that I have somehow managed to preserve all my leg muscle while dropping 20lbs. In fact I'm confident that my legs have accounted for the majority of lean muscle that I have lost during the transition from weights to calisthenics. This isn't a bad thing though, because now normal pants fit my quads, my butt isn't distractingly large, my adductors don't chafe, I can run much faster, and overall, my athleticism has improved greatly. I don't think you can beat weights for pure size and strength for the legs, but without a doubt, you can build significant strength and stimulate hypertrophy to get you some athletic legs using only your bodyweight.