GJ "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world."

Or if Archimedes had been a BJJer "Give me a grip and a joint on which to twist and I will submit anyone". We did a lot of wrist/elbow/arm throws. These throws take advantage of leverage (and proper body) mechanics to throw a person, but without directly interacting with the hips or legs (i.e. the anatomy that keeps one vertical).

• Kote gaeshi Attach two hands to partner's one hand. Both thumbs on the back (dorsum) of their hand while gripping the meat of the thumb and pinky (thenar and hypothenar eminence). The throw is composed of twisting the palm of the hand outward and to the floor, while pulling it to your center of mass (COM) and away from theirs ("peanut butter jar concept"). Stepping is 180^o either stepping to the outside and following their forward motion or wrapping (putting your butt on their hip) in opposition to their movement. This throw works well off pushing, grasping, and grips, but is hard off punches. Also works well when people take a stab or swing with a knife or club.
  
• Kimura off the spear, elbow the head with the centerline elbow, and grab the wrist ACROSS then to figure 4 (and pointed up). To throw make a "scoop" a la small circle jujitsu, rather than pushing to to floor, suck the elbow toward you while pushing the wrist to the floor. We worked this both with a haymaker and a club attack.
  
• Americana off the spear, elbow the head with centerline elbow, and grab with the same side wrist to figure 4 (hand pointed down). As above but a "backwards" set-up.
  
• Ikkyoplace both hands on the outside of your partner's. Cross hand at the wrist, same side hand just proximal to the elbow. Now either pivoting away or stepping 45^o across the trajectory of your partner while rolling hands forward and down to place them bent at the waist with arm extended out from side. To finish throw either walk them straight into floor or drive corkscrew into or away from them (tenkan vs. irimi).
  

Continued working on a new ground flow from the guard

Use the arm drag to place partner's arm across body with wrist in arm pit.

Set-up arm bar, placing wrist bone proximal to elbow for leverage.

Can't pivot?

OK trap crossed arm with body, hook under leg and with trapping side hand and grab lat with other hand go to (dead) flower sweep.

Defends sweep by basing across with free hand

Go right back to arm bar

Grabs head and stacks

Is cool, go to "bench press" (or "leg press assist") arm bar and push on knees to extended, alternatively walk out on shoulders and lock free hand (most likely hooked around your neck if he's stacking) with scoop armbar

Any other options?

Sure as this is stolen from Marcello Garcia, use the arm drag to take the back.

But what if they defend the arm drag?

Well that's fine, too. They'll probably jerk the arm back and away, if you see this reaction, fake the arm drag and go right to hip bump (open the guard, catch the tricep and make a tripod with the other hand).

OK so I "sorta" got the arm drag but they pulled the hand out, now what?

Depending on the clearance of that arm, I'd either attack with triangle or oma plata, but both these have to be loaded and then followed by hip repositioning.

But its all dependent on the arm drag

Not really very similar position is available if you pop the elbow in and hook your knee over their shoulder, in a quasi-triangel position.

But but what if...

Geez settle down, its just a flow pattern to work some different moves with

Lastly we worked some movement drills, essentially using the triangular foot work so prevalent in kali, capoeira, tai chi and pretty much every other combat art known to man (or woman). Just imagine the mighty samurai coasting from foot to foot...

• The boxing defense -- quarter circle from and aggressive to the outside of his weak hand, as you clear the line, set up a cross/hook/tiip/kick.
  
• Cutting the ring -- as you quarter circle, he cuts the circle by crossing your line (say throwing a wide hook), change directions with a pivot step back and away across toward his strong side. Be ready to attack or cut either left or right depending on his next move.
  
• Angling on kicks:
  

  
  

  J-Kick
  

  Step with lead foot off angle (outside his rear foot) while throwing jab, follow with rear kick.
  

  Triangular step with rear foot (outside of his lead foot)while throwing jab, follow with lead kick.
  

  J-C-Kick
  

  Advance with jab, step off angle with cross (outside his rear foot), follow with lead kick.
  

  Advance with jab, triangular step with cross (outside lead foot), lead kick.
  

  
  In any case the alternating lead-rear set-up has several reasons for its strength (1) loading -- the body mechanics of the previous strike set-ups the next, (2) "blender action" -- your trying to catch the person between the onslaught of all your available tools (i.e. the center line), and (3) increased shot percentage -- is easier to evade attacks on the same side just keep moving to the outside line on that side.
  
• Four count combinations are a great way to work on angling, make your shoulders clear on either side as you kick, working across the center or around the body with the punches.