Shape memory alloy heat engines and energy harvesting systems

A heat engine, comprising:

• a first rotatable pulley;
• a second rotatable pulley spaced from the first rotatable pulley;
• an idler pulley spaced from the first rotatable pulley and the second rotatable pulley;
• a shape memory alloy (SMA) element disposed about a portion of the first rotatable pulley at a first radial distance and about a portion of the second rotatable pulley at a second radial distance, the first and second radial distances defining an SMA pulley ratio, wherein the SMA element includes:
• a first end;
• a second end;
• at least three loops, wherein each of the at least three loops circumscribes the first rotatable pulley, the second rotatable pulley, and the idler pulley;
• a first joint joining the first end to one side of the at least three loops;
• a second joint joining the second end to an opposing side of the at least three loops;
• a timing cable disposed about a portion of the first rotatable pulley at a third radial distance and about a portion of the second rotatable pulley at a fourth radial distance, the third and fourth radial distances defining a timing pulley ratio, the timing pulley ratio being different than the SMA pulley ratio;
• wherein the SMA element is configured to be placed in thermal communication with a hot region at a first temperature and with a cold region at a second temperature lower than the first temperature;
• and
• wherein the SMA element is configured to selectively change crystallographic phase between martensite and austenite and thereby one of contract and expand in response to exposure to the first temperature and also to one of expand and contract in response to exposure to the second temperature, thereby converting a thermal energy gradient between the hot region and the cold region into mechanical energy.