Unicellular parasites have developed sophisticated swimming mechanisms to survive in a wide range of environments. Cell motility of African trypanosomes, parasites responsible for fatal illness in humans and animals, is crucial both in the insect vector and the mammalian host. Using millisecond-scale imaging in a microfluidics platform along with a custom made optical trap, we are able to confine single cells to study trypanosome motility. From the trapping characteristics of the cells, we determine the propulsion force generated by cells with a single flagellum as well as of dividing trypanosomes with two fully developed flagella. Estimates of the dissipative energy and the power generation of single cells obtained from the motility patterns of the trypanosomes within the optical trap indicate that specific motility characteristics, in addition to locomotion, may be required for antibody clearance. Introducing a steerable second optical trap we could further measure the force, which is generated at the flagellar tip. Differences in the cellular structure of the trypanosomes are correlated with the trapping and motility characteristics and in consequence with their propulsion force, dissipative energy and power generation.