The law on being no-balled for throwing is fairly straightforward. It is the angle of the elbow joint just prior to the point of release compared to the angle of the elbow joint just after release that matters. It doesn't matter if the elbow joint is bent prior to release as long as it stays at the same angle on delivery.
This is the claim made regarding Muthiah Muralitharan the Sri Lankan off-spinner. I disagree and for very good personal reasons. This article is written, by coincidence may I say, just after Umpire Emerson no-balled Muralitharan in the one-day match against England.
The Sri Lankan captain objected to the umpire exercising his right of control of the game by huffing and puffing and taking his team off the field. Incidentally, if he is allowed to do this without fear of retribution, what next? Take your team off when you do not like a LBW decision?
I say I speak from a personal point of view because due to mainly bowling for over 40 years and having very loose joints, I now have an elbow permanently bent at almost the exact same angle as Muralitharan. I do not however bowl off-breaks. If I did I should be no-balled for throwing. I bowl seam-up and can keep my elbow joint at the same angle through delivery.
I can do this mainly because of the position of my wrist. If my wrist is kept in a position that keeps the palm of my hand facing the batsman then everything is ok. However as soon as I turn my palm back away from the batsman, it is impossible for my arm (which, remember, is always bent), not to bend even slightly further from its original angle. This means that although my arm will not completely straighten, it must straighten out back to its original angle at the very least. This is still a throw.
Muralitharan has a very flexible wrist but the very action of turning his wrist backwards from the target can only increase the necessity for his arm to bend more at the elbow. When you have a permanently bent elbow joint, it is an physical impossibility for the elbow not to bend more away from the straight in such a situation.
The journalists for example who say that his arm cannot straighten on delivery simply do not understand a) what a throw is and b) what bowling is about. Many of these journalists have not even played cricket, even at decent club level.
I've read an article by Ian Chappell who says "In any case , he (Muralitharan) is really gaining any advantage so what does it matter?" That's ridiculous! The purchase and pace one can achieve by using a throwing type action on an off-break is considerable -- try it. I have.
Poor old Murali though I am sure is not deliberately throwing, he just bowls that way and even if his action is illegal as I believe, it still takes a considerable amount of skill to land it in the right place. But he does throw!