This is from a recent video I took and blog post. To sum up, I think learning the complex hand patterns of traditional TJQ seems to hinder progress. I came up with/modified these as an attempt to teach intuitive structured body movement very early in ones training. So far, people have found it useful. Anything to add?
Here are three types of push hands exercises that are designed to get people to use their hip joints and encourage free play. They are all forms of what I now call "static hands" drills in that the hands/arms maintain the same contact point with the other person. Keeping these fixed hands positions intentionally limits any sort of parrying motions of the arms, and is a good indicator of/way to develop functional structure and root.
The first is a form of single hand push hands minus any major intent to push the other person back. The focus should be to roll around the person's incoming force and get into a better position while staying grounded. Basically, we're just practicing ward off/peng energy here.
The second is a static hands drill designed to teach people how to push someone out of their stance in response to pushes they received. For this drill to work it is important not to be too light with the hands or disconnect them at any time. We're not practicing parrying here but learning to move the body while staying structured and rooted. This drill in particular seems to give people a good foundation for free play rather quickly. In fact, I've shown this drill to people who have had years of competitive push hands experience, and it was clear they could use this drill to improve as they had trouble with other less experiences than they were. There is little room for error. You can't save yourself by using some flailing arm motion. You either have structure or you get pushed back.
The third static hands drill is an expansion of the second, using the starting hand position used in competition matches. Because the shoulder joint is freed up a little bit more, a couple more techniques can be used, e.g. rollback and elbow.
These drills are simple enough, I hope, for people who don't have access to a teacher to try on their own. They can get the idea of what it's like to play in Taijiquan, and build some foundation skills that would allow them to hold their own against people in many push hands meetup groups. They're also nice to use when people from different schools used to different rules sets of free play want to find an easy way to practice together and not have to argue about rule sets. No teacher? No excuse. No Taoist philosophy? No problem. Grab a buddy and play!