As the 'mechanics' of Medieval battle, so to speak, are pretty comparable to that in Ancient warfare (not to mention that medieval sources don't seem to really talk much about the 'mechanics' of fighting) I think I can help you out here by using examples from the Classical world. /u/WARitter mainly talks about the methods used by Medieval soldiers to identify friendly troops. So I'll give some detail on the actual mechanics of fighting and how that could and often did result in "friendly fire".

There were lots of ways to die in ancient or medieval fighting other than being transfixed or beaten to death by an opponent. For one, it was a phenomenon of the 'rout' stage of a battle that soldiers might deliberately attack men of their own side, in wild panic or in a more deliberate attempt to clear a path. This phenomenon pops up in literary accounts of the conduct of wild, terrified troops. Livy gives a few examples of this phenomenon (and probably quite a few more). Here's an example from a battle between the Romans and Gauls in 350 BC under the consul Marcus Popilius Laenas, from Livy Book 7.24:

"...the Gallic host, superior to any feeling for such losses, sprang up like a new army, and urged their fresh troops against the victorious foe".

At this stage the battle had been going on a while. The Romans were nearing exhaustion and the consul rashly exposed himself during the fighting, and got a javelin in the shoulder for his trouble, forcing his guards to take him off the field to dress the wound. But once he had done this, he rode back to the front and re-invigorated his troops, who:

"drove back the foremost of the Gallic maniples, and then, forming in wedges, burst through into the midst of the main array...barbarians thrown into confusion, having no definite orders nor commanders and, turning, charged upon their fellows."

In this example, the section of the Gauls whose nerve broke first actually charged a body of other Gauls to clear a path for their escape. We might imagine that this might have resulted in a number of 'friendly fire' casualties, especially if the Gauls receiving the charge really tried to stop the runners. This appears to have been a relatively common occurrence in battlefield routs. A more viscereal depiction of this phenomenon can be found in Polybius' description of Zama in Book 15.13, after Hannibal's front line of mercenaries had broken and tried to get away from the Romans through their own second line:

"...the [Carthagingian second line] by contrast shrank back in cowardly fashion and failed to support the mercenaries. The result was that at last the [mercenaries] themselves gave way; it seemed to them that they had been abandoned by their own side, and so as they retreated they turned upon the soldiers in their rear and began to cut them down. This action forced the [second line] to die bravely in spite of themselves, for when they found they were being slaughtered by the mecenaries, they were obliged quite against their will to fight both the barbarians and the Romans at the same time: when they had been brought to bay they defended themselves with desperate courage and killed a great number both of the mercenaries and the enemy."

'Friendly' casualties could occur during partial routs as officers used violence to compel men to stand and fight. Standard bearers and centurions were particularly liable as targets of exemplary punishment for their decisive role in motivating most soldiers to stand their ground (Livy 2.59). In the Battle of Apulia of 294 BC against the Samnites, after an inital flight the Roman consul Marcus Atilius formed up his cavalry at the entrances to the Roman camp with spears levelled, so that the Roman soldiers had the choice of going back to the fight or physically fighting the consul and cavalry. I can't find the specific sources at the moment, but I am fairly sure I have read of at least one example of an officer killing a standard bearer during battle to set an example. Sidebottom (2004, 109) for instance takes it for granted that officers on occasion killed fleeing soldiers. The role of coercive violence in forcing armies to fight, even the vaguely 'democratic' Mid-Republican Roman armies, make it not hard to imagine that in the heat of battle violence might occur between officers and men whose fear of the enemy has overwhelmed their shame and respect for authority. Indeed, this is why the Romans put the Centurion's second in command, the optio, at the back of maniples and cohorts, with a big stick in their hands.

Combatants could die during routs, and no doubt during the press of fighting but especially during routs, due to 'crowd-crush' or being trampled. Livy provides another example of this occurring in Book 10.28, after an impetuous commander by the name of Decius committed his cavalry to an unfavourable engagement against more Gauls:

"Twice they compelled the Gallic cavalry to gave way. At the second charge they advanced nearer, and were briskly engaged in the midst of the enemy’s squadrons, when, by a method of fighting, to which they were utter strangers, they were thrown into dismay. A number of the enemy, mounted on chariots and cars, made towards them with such a prodigious clatter from the trampling of the cattle and rolling of wheels, as affrighted the horses of the Romans, unaccustomed to such tumultuous operations. By this means the victorious cavalry were dispersed, through a panic, and men and horses, in their headlong flight, were tumbled promiscuously on the ground. The same cause produced disorder even in the battalions of the legions: through the impetuosity of the horses, and of the carriages which they dragged through the ranks, many of the soldiers in the van were trodden or bruised to death."

This had also happened in the battle I mentioned before in 350 BC against the Gauls: while the Gauls stiffened up later, they had started the battle by trying to attack the Romans uphill, which went poorly:

"[The Gauls who had] fallen upon one another wrought greater carnage then even their enemies had done; for so headlong was the rout, that more were trodden under foot than slain with the sword." (Livy 7.23).

I cannot personally think of many instances where 'friendly fire' is specifically mentioned to have occurred in ancient battles during the actual fighting, though I'm sure mistakes did occur, especially with missile weapons which could be used heavily in all stages of Roman-era warfare (Plut. Sulla 18-9) For more information on this continuous missile-warfare even during close-combat, see Zhmodikov, "Roman Republican Heavy Infantrymen in Battle (IV-II Centuries B.C.)," 2000. There may be examples of friendly fire from missiles in the literature, I just can't think of any.

As Ancient and Medieval warfare were waged with basically the same technology and the 'mechanics' of infantry and cavalry battle in these eras are basically the same, even if they might be different in context, scale, appearance, etc, I think all of these examples I have provided must have occurred in Medieval battle as they certainly did in Ancient battle. Soldiers whose fear of the enemy has overwhelmed them may attack their own side accidentally or deliberately. Tactical developments may cause one or even large numbers of men to be knocked off their feet and be crushed in the fighting. Officers may deliberately and conspicuously kill their own soldiers to set an example to the rest. And without doubt, when javelins were thrown and arrows fired over the heads of engaged troops, which may have been a common occurrence, there is no question that occasionally a friendly would be struck by a missile. I hope this helps answer your question.

EDIT: Just as regards your specific concern for accidental "friendly fire" from sharp weapons, I'll note that it was a particular concern for the Romans to maintain an open formation so that soldiers could use their sword and shield properly, and it would be helpful for throwing pilum too. For example, Caesar at the Battle of the Sabis in 57 BC had to order some of his troops to "...open ranks, so they could use their swords more easily." (Caes. Bell. Gall. 2.25). We might assume that, as they required space to use their sword and shield properly, being in ranks that were too condensed would logically increase the risk of "friendly fire" from swords. Unfortunately, I still can't think of any specific examples of soldiers inadvertently being hurt by the sharp weapons of a comrade during fighting. Still, that idea could easily be applied to Medieval soldiers fighting with swords too.

I am no historian, but I have seem this question brought up before. One answer that's specifically about medieval battles that I know of is this

Edit: forget to tag the author, /u/WARitter, who provided such a thoroughly researched and well-put-together answer.

I would imagine that this is not terribly well tracked in most medieval sources.

So as a follow-on question, I'd love to ask: when did the military (of any country) start tracking friendly fire vs. other sources of casualties (such as battle injury, disease, malingering, etc.)?

Hey There!! So there is one incredibly famous incident of friendly fire from the late medieval period, the Battle of Barnet in the Wars of the Roses. Let me take you through that battle and then leave some general discussion points and you all are welcome to follow up if you like.

The Battle of Barnet was fought in the middle of Edward IV's reign, after his unpopularity and nepotism had driven the Earl of Warwick (one of the most powerful noblemen in the country) to change sides and restart the conflict between Edward IV's Yorkists and Henry VI's Lancastrians. Edward IV had been driven out of the country and was returning to reclaim his throne. Warwick on the other hand, had struck a deal with the Lancastrian queen Margaret of Anjou, the real head of the Lancastrian faction to reclaim her family's position and her son's succession.

As for the battle itself, there are several things we know with certainty. First off, most chronicles agree that the Yorkists were fairly outnumbered and that Edward IV was aware of this fact. For this reason, he intended to close the distance between the armies and try to surprise his enemies. The results was an early morning battle with lots of fog on the battle field.

At this point, it is worth saying that I feel confident the Yorkists had a far more cohesive leadership structure than the Lancastrians. Edward IV was a the model of a "warrior-king," incredibly charismatic, with a deft understanding of how to press local advantages in formation and tactically array his army. His right flank was command by his ever-loyal brother, the Duke of Gloucester, and the left flank by his close friend, Lord Hastings. The Lancastrians, despite their numerical advantage, had greater issues in terms of cohesive command. Henry VI was no one's idea of a competent king, or really a competent anything. He was indecisive and dithering, at least when he wasn't suffering from mental breakdowns. Far from leading as a battlefield commander, he was also a prisoner of the Yorkists at the onset of the battle. The Lancastrians were a hodge-podge arrangement of old enemies. The Earl of Warwick and his brother, controlled huge resources and armies, but were latecomers to the cause, viewed by suspicion from by diehard Lancastrians like the Earl of Oxford. Warwick had spent a good part of his life fighting the Lancastrians, feuding in particular with Henry VI's favorite cousins, the Beauforts. These suspicions were not meaningless aristocratic feuding, in this period it was extremely common for factions to change sides, even mid-battle. This would prove to be a huge issue as the battle played out, as it could affect the morale of soldiers on the front lines.

The Lancastrians started out with a fairly decisive advantage and the early phase of the battle played in their favor too. After exchanging projectile fire, the armies waded through the fog to engage in the melee with polearms. The Earl of Oxford (commanding the Lancastrian right) routed his opposite number, the Lord Hastings, driving him off the field completely and back to the village of Barnet. Oxford then struggled to reorganize his men and stop them from simply looting the town to return to the battle.

However, given the wide disposition of the armies, low visibility, and lack of command cohesion, Oxford's rout of Hastings had not really impacted the battle overall. Lord Montagu (Warwick's brother) and Edward IV fought to a standstill in the center. But on the Lancastrian left (Yorkist right), Gloucester began to overwhelm the Duke of Exeter, whose forces began to panic, but their collapse was somewhat slow. The effect of this was that the orientation of the battle turned drastically from how it had started.

At this point, the Earl of Oxford returned with some of his men, attempting to find his way through the fog to hit the Yorkist rear and flanks. However, he did not know and could not see the re-orientation of the armies, meaning he ended up approaching flank of Montagu's center. The Lancastrians then mistook Oxford's "star with rays" banner for the Yorkist "sun in splendor" banner and, assuming that Edward IV had committed his reserves, proceeded to order arrow volleys on Oxford's men. Both sides then panicked, Oxford's men assuming treachery by Montagu and Warwick, and Montagu's men assuming a flank attack by the Yorkists. This chaos broke down the discipline of the Lancastrians, and Edward IV, sensing victory, then actually committed his reserve. The result was a decisive Yorkist victory, the deaths of Warwick and Montagu, the capture of Exeter, and the escape of Oxford (who would later join one Henry Tudor).

I hope this example was somewhat helpful in illustrating how friendly fire could happen in a medieval battle. I think there are a couple of key things to keep in mind when looking at "friendly fire" works in this period. First of all, most armies worked on concepts of formation and morale. You weren't necessarily looking to stab every person in the opposing army to death, but to break their discipline, cause them to flee (possibly killing each other as they do) and redeploy cavalry to run them down as well as harry survivors to prevent them from regrouping. This cavalry charge was devastating during the rout, and as such pitched battles were considered incredibly risky by most commanders. This is partly why formations are considered so important, ensuring that for the most part, the individual soldier is focused on fighting the man straight ahead of him, knowing that he has friends to his left, right, and back. This is also why in the pre-gunpowder era, there is such an emphasis on flanking and hammer-and-anvil type of tactics, because when soldiers start to fear attacks from an unexpected direction, they panic, running over each other to try to escape death in the rout.

I thought about putting another point on projectile warfare, but this is already running a bit long and so I think I'll just summarize my points here. There were most likely (almost certainly) incidents of individual soldiers accidently or intentionally killing men "on their own side." This would happen especially during the rout, when discipline broke down and survival instinct superseded tactical thought. It is harder to say to what degree "friendly fire" occurred during the melee phase, as most medieval chroniclers and sources don't really cover the mechanics of battles. Some experimental historians have attempted to reconstruct these situations and most theories tend to lean on the fact that formations were developed to prevent exactly this sort of thing from happening on an individual level in order to maintain the discipline and morale of the soldiers. However, we do have chronicled evidence from battles like Barnet, where betrayals and mistakes occurred on this type of formation level. Hope this helps and I will do my best to help if you have follow up questions.

Sources:

The Military Campaigns of the Wars of the Roses by Philip Haigh, 1995

Warwick the Kingmaker by AJ Pollard, 2007

The Wars of the Roses by AJ Pollard, 1988

Arms, Armies and Fortifications in the Hundred Years' War edited by Anne Curry and Michael Hughes, 1994

Medieval Warfare: A History by Maurice Keen, 1999

You may be interested in a (somewhat) similar question which I asked (albeit specifically about ancient battles and formations of spearmen) here. /u/Iphikrates gave me a wonderful answer.

Hope this helps!

Wondering if I can ask a follow up to this...

Is there a documented "first case" large scale friendly fire incident in the post firearms era?