I found two good articles on this topic, and since this question gets posted over and over, I thought I would summarize them here and hope it will help you with your training.
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There are two primary elements for improving your fighting power and speed:
a)perfect your techniques with perfect repetition: This means practicing your punches and kicks over and over (thousands of time) to firmly engrain the motor skills into your neuromuscular system. The less you have to think about a technique, the faster you can do it. Additionally, the more perfect your technique the more power you generate for the same amount of effort (think of it as leverage). You also want to practice at full speed once you have the basic technique, to ensure the adaptation to a technique is to how you will actually use it.
b)improve overall (large) muscle strength: Stronger muscles produce more force, and more force = faster, more powerful movements. Thus, general strengthening of your major muscle groups (esp. hips and core) will help you to perform your techniques more explosively and hence generate more speed and power. You'll want to ensure you are training matching muscle groups (i.e. quads and hamstrings) as:
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Current research suggests that strengthening opposing muscle groups (agonists and antagonists) enhances movement speed (Jaric, Ropret, Kukolj and Ilie 1995).
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Thats pretty much it. You might also add in body composition improvements (reduce your % body fat), but the biggest improvements over your base speed/power are going to be via the two points above, most notably learning and perfecting proper technique with large amounts of repetition. Conditioning of course also factors in as far as being able to maintain your improved speed/power over the course of a fight.
Regarding some of the common thoughts about punching/kicking with weights (besides imo being an invitation for connective tissue damage), the one article notes the following:
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investigations into the effects of using weighted shoes and ankle weights found that the groups who practiced without the weighted devices actually improved their speed more than the experimental groups who practiced with the weighted devices.
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The reason:
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If a skill is to be performed at a given speed, it should be practiced at that speed in order to facilitate the learning of the skill. By practicing a skill at a slower speed than would normally be used in the performance of the skill, you’re training your neuromuscular system to perform at a slower speed...
Consider fighters who throw punches while holding onto dumbbells. Will their punches with the dumbbells be faster, slower or the same as their punches without the dumbbells? Obviously, their punches are slower. Therefore, it follows that the use of weighted implements actually impairs the learning of sports skills.
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Not to mention the risk of damaging your joints. Anyway, hopefully this will put that recurring question to rest. More details in the first article linked below which discusses how punching with weights create an illusion of improved speed....
What about plyometrics? The easy answer is that there has been no credible research that shows plyometrics to improve speed better than standard strength-training, and that plyometrics carry an extremely high risk of injury potential.
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a large number of research studies have concluded that plyometrics are no more effective than regular strength-training activities when it comes to improving speed, power and explosiveness
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Links to supporting articles are here:
http://www.timferriss.com/improving_speed.html
and here:
http://www.eliteathletetraining.com/...Article_8.aspx
Hope that helps!