Bodyweight training is an effective way to build strength. It addresses both the muscles and the surrounding connective tissue. Push-ups, pull-ups and dips are foundational exercises for the upper body. However, these exercises have applications beyond strength development. They can be used to cultivate power, too.
Power and Plyometrics
According to the American Council on Exercise, plyometric exercises are an effective means of training for power, leading "to improvements in vertical jump performance, leg strength, muscle power, acceleration, balance and overall agility." They're a staple of professional and Olympic athletes. To maximize their benefits follow two simple rules. One, make sure you've been strength training for at least a few months to minimize the risk of injury. Two, keep the volume low and the quality of movement high.
Integrate clapping pull-ups and clapping push-ups into your routine a couple of times of week. Keep the repetitions between 3 and 10. Focus on being light and fluid in your movements. Do two to three sets before intensive strength work. Since both exercises address triceps power, you can perform dips in the usual way for strength training. As with any program using plyometrics, seek professional supervision.