Men who kill their families can be separated into four distinct types.
British criminologists have made the assessment after studying newspaper records of "family annihilator" events over the period from 1980 to 2012.
A family break-up was the most common trigger, followed by financial difficulties and honour killings.
Writing in the Howard Journal of Criminal Justice, the team lists the four types as self-righteous, anomic, disappointed, and paranoid.
Each category has slightly different motivations and many cases also have a hidden history of domestic abuse. In four out of five cases the murderers went on to kill themselves or attempted to do so.
The research revealed the most frequent month for the crime was in August, when fathers were likely to be with their children more often because of school holidays.
The cases have also become more common with more than half occurring since the year 2000. Only six cases were found in the 1980s.
One of the study's authors, David Wilson of Birmingham City University, UK, said a reason for this increase could be "men feeling they need to exercise power and control" over their family.
It was often men who had invested "too heavily in a very stereotypical conception of what it means to be a husband and a father within an institution called a family", Prof Wilson told BBC News.
"Their view of the family is very black and white, and doesn't reflect the increasingly dynamic role that women can play in the economy and in the institution of the family itself."
He added: "The thing that struck me was the kind of extraordinary ways that men thought up to kill their children.
"They jumped from bridges with children in their arms; they drove into canals with children in the backseats. These were extraordinary histrionic, controlling ways of committing murder.
"This was a group of men who were not in any way previously known to the criminal justice system. This is a very different profile of male murderers than we normally find in criminological research."
The new study differs from previous explanations for the family killer. These have pointed to revenge or altruism as causes or that an incident leads a man to snap. But Prof Wilson's group said these explanations were not reflected in many cases they reviewed.
He explained that the private nature of some families could be a reason why fathers had seemed loving fathers and dutiful husbands.
For this reason, he added, it was important to take domestic violence seriously and encourage "more people to become aware of other people's lives".
Keith Hayward, a professor of criminology at Kent University, was not involved with the new study.
He said that it was valuable work that other researchers could further develop, but constructing "typologies" from second-hand media reports was problematic, and "not always helpful for policy development".
"There are a number of ungrounded assumptions going on about 'motivations'. This is reflected in the four categories, which overlap and thus don't seem that rigorous to me."
Prof Hayward recognised that getting access to the killers was in many cases impossible, but without detailed insight into their life histories, "it's all inference", he said.
The researchers did state that there were disadvantages of using only newspaper reports, but argued that interviews with family members "lifted a lid on the reality of life behind closed doors" which helped determine possible motives.
The study found 71 cases of the family annihilator, with a small minority of 12 women which the team will follow up with future research.