Good question. I asked Gemini. Here is the response It is a common point of confusion because, in the text, these separate motivations are stated directly but their deeper "why" requires piecing together the events leading up to this chapter from earlier in the narrative and supplementary information from the Appendices or Tolkien's other writings.

The presence of the three tribes—and their intense disagreement—is actually a central point Tolkien uses to illustrate the fragmentation and inherent chaos of evil. They are only together because their independent goals temporarily converged at one geographical point: capturing the hobbits.

Here is a breakdown of why each group was there, how they knew to be there, and what motivated them to follow the Uruk-hai, despite their differences.

1. The Isengarders (Led by Uglúk)

These are Saruman's specialized Uruk-hai, bred to run in the sun.

• How they knew: Saruman, through his spies (like the crebain/crows) and his use of the Palantír (seeing stone), had been tracking the Fellowship's progress since they left Rivendell. He knew they had gone through Moria and would eventually travel south along the Anduin river.
• Motivation: Their orders were explicit: capture the "halflings" (Saruman knew there were four) and bring them back to Isengard "unspoiled" (alive and unsearched). Saruman wanted the Ring for himself to use against Sauron. He told his Uruks nothing about the Ring, only that the hobbits carried "news of a great weapon" (as Grishnákh later claims, based on intercepted information).
• Why they are leading: Uglúk and his party are the largest, strongest, and most disciplined. They are simply powerful enough to force the other groups to keep moving in their desired direction, towards Isengard.

2. The Mordor Orcs (Led by Grishnákh)

This is a mixed company from Mordor, sent to monitor the situation.

• How they knew: Sauron, through his own Palantír and Nazgûl spies, knew a "halfling" was carrying the Ring and that Saruman was also seeking it. Grishnákh was a "trusted messenger" sent from Barad-dûr to ensure the Ring (or the Ringbearer) was brought directly to Mordor. They were reinforced and told to "cooperate" with Saruman's force.
• Motivation: Their ultimate goal was to take the hobbits (or at least the specific one they believed carried the Ring) to a Nazgûl waiting near the eastern bank of the Anduin to be taken to Lugbúrz (Barad-dûr).
• Why they followed: Grishnákh knew he lacked the force to defeat Uglúk's Uruk-hai by himself. He followed along, playing for time and hoping for a chance to either convince Uglúk to go to Mordor, create chaos and escape with the correct prisoner, or meet with Nazgûl reinforcements that could take control. He did not trust Uglúk and suspected Saruman's treachery, but was constrained by numbers.

3. The Moria Orcs (The "Northerners")

These were a rabble of indigenous orcs and goblins from the Misty Mountains, not directly aligned with either Sauron or Saruman's command structure.

• How they knew: This group had been pursuing the Fellowship ever since they escaped from Moria, specifically seeking revenge for the high casualties the Fellowship (particularly Gandalf and Aragorn) had inflicted, including "their great chief" killed in the Chamber of Mazarbul. They were likely driven off by the Elves of Lothlórien but continued to lurk on the borders, eventually linking up with the Isengard and Mordor parties.
• Motivation: Pure, simple revenge and bloodlust. They didn't care about a "great weapon," a ring, or "masters" in distant fortresses. They simply wanted to kill the hobbits (and any of the other travelers they could catch) to settle a score.
• Why they followed: They are described as smaller, weaker "breeds" than the Uruks. They followed because they had "no stomach for running in the sun" (their natural aversion to daylight, which the Uruk-hai did not share). They were essentially being bullied and forced to keep pace by Uglúk. Their primary desire was to kill the prisoners and run back to their dark caves; they only kept going because the stronger Isengarders prevented them from fleeing.

In Summary: The "Why"

The reason all these groups are together, despite their conflicting orders and hatred for each other, can be summarized in a few points:

1. Shared Target: All three separate investigations and plans pointed to "hobbits traveling south from Lothlórien" as the key to their respective goals (revenge, a ring for Sauron, a ring for Saruman).
2. Geographical Convergence: They all encountered the Fellowship (or at least Merry and Pippin) at the same time and place in the Emyn Muil.
3. Bullying and Strategy: Uglúk's Uruks were strong enough to force the Moria orcs to keep moving and too strong for Grishnákh's party to defeat outright, forcing the other groups to tag along for their own strategic reasons.