State Senator Dan Patrick (R) of Houston, Texas is almost a living caricature of how not to shake hands. If it wasn't so sad - it would be funny. First off, when it's reasonably possible, if you're at the podium and you're introducing someone - step out from behind the podium. It's not about you - it's about them. Don't pull them into you either - your arm should be extended, but not over reaching. Mr. Patrick also looks like he's giving former Governor Sarah Palin (R) Alaska, a traditional "feminine-style" hand position - with is hand cupped and not fully opened (Sidebar: a traditional feminine handshake should NOT be used in a business/political/leadership setting - otherwise ladies, the men won't take you seriously). In addition, he is being overly dominant in twisting his hand so that it is on top of her's. If you're a state senator, you should be very aware of the pecking order - and present your hand in the vertical plane, perpendicular to the ground (Remember, Sarah Palin is a former Governor and VP Candidate. Mr. Patrick is very much her junior.). Another error, the most noticeable one here is - don't invade the other person's personal space. It's too dominant when you're introducing a superior and most women will consider it an unwelcome advance or at least, very chauvinistic. It's one thing to stand too close, it's another to lean in - almost as if you're going to kiss them. Your job is to make the other person feel welcomed and to (hopefully) develop some rapport. Whew .... I'm getting tired. Don't grab anyone's elbow, arm or shoulder unless you are truly well acquainted, and never in front of an audience. Again, it is disrespectful and patronizing.
Sarah is doing a pretty good job compensating, certainly better than most - but notice the obvious "pull back" and twisting of her upper body. For her part, Palin should have her left hand/arm free - or at the very least her phone should be put away and her tablet better arranged. Such choreography would have allowed her to "square-up" and face Patrick with her whole body - thus she'd be displaying less defensive/beta behavior, superior bonding would be possible and the better able she would be to deal with this over-compensating alpha male in a more "momma grizzly" manner.