What were the main conflicts leading to the necessity of the constitutional convention?

In my mind, there were conflicts over the issue of representation, slavery, and the notion of what it means to be free.  In terms of the representation debates, the larger states sought to advocate the Virginia Plan, which determined the issue of representation through population.  The smaller states advanced the New Jersey Plan, which suggested an equal number of representation for each state.  The compromise was Sherman's Great Compromise, which established a bicameral legislative branch consisting of one House of Representatives which was driven by population and one Senate which was to be driven by a fixed number for each state.  The issue of slavery was addressed by the delegates through the deeming of the slave population as 3/5 of vote, allowing Southern states to count their slaves towards the population, allowing the North to ensure that slave representation was limited, and ensuring that people of color were seen as less of a person.  It also called for the slave trade to continue to 20 years and then the federal government would control it, ensuring that the framers lacked courage and conviction on the most pressing social issue of the day.  Finally, the debates between federalists and the anti- federalists helped to configure what it means to be free in the new nation.  The former believed that individual freedom meant little, if anything, if the entire structure of government and social order could not ensure domestic security and a sense for control.  The latter argued against this, in suggesting that one of the primary reasons the Revolution was fought was to ensure personal freedom away from a tyrant- like centralized authority.  To have swapped one repressive element for another is not logical.  Both sides were appeased with the Constitution's strict demand of being the supreme law of the land with the addition of the first ten amendments, driven to guarantee personal security.

Good luck: )