measures (the angle of knee and ankle joints) OR(the angles of knee and ankle joints)

I am talking about two sensors for two measurement from a knee joint and an ankle joint.
Thanks

[AmE - not a teacher]

I think this is a great question, because there are many ways to write this, all with subtle differences. Your goal should be to remove ambiguity, so I think you should favor in the side of caution. I might write something like

... measures the angles of the knee joints and the ankle joints.

I think either would be understood but your alternative would, as you say, remove any ambiguity.