Bioresorbable new terpolymers of L-lactide, glycolide, and trimethylene carbonate with different compositions were synthesized via ring-opening polymerization reaction of the cyclic monomers using low-toxicity zirconium(IV) acetylacetonate as initiator. The thermal and mechanical properties were investigated by means of thermogravimetry, differential scanning calorimetry, stress-strain measurements, and dynamical mechanical analysis. The glass transition temperature of the terpolymers changes with composition from 12 to 42 degrees C in a predictable manner. All terpolymers display shape memory properties and, after undergoing 100% deformation, they recover the permanent shape in a time frame of seconds. Terpolymers with high L-lactide content show a glass transition in the range of 38-42 degrees C, recovery temperature close to body temperature, and good recovery ratio (>0.89). Low-toxicity bioresorbable terpolymers with shape memory properties are promising new materials for biomedical applications.