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As a general rule, leg sweaps and trips aren't really effective
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leg trips, reaps are very effective. If they are not working for you then you are not doing them correctly.
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my strategy is to give up my own balance in order to throw uke. Because my balance is gone, I do often end up on the ground, but not necessarily grappling
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You should not give up your own balance while doing sacrifice throws, you should yield, there is a difference. Often in order for these to work you need to pull uke sharply towards you first to get them off balance, kuzushi. Rarely will uke just happen to be leaning way forward for you to execute them, you have to create off balancing not just wait for it.
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there is a style of koshinage that uses the leg instead of the hip to block uke's movement to cause the throw
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that would be Harai-goshi in Judo, "sweeping hip throw". Ideally you use both your hip and the sweeping motion of the leg simultaniously.