Repeated mechanical failure due to accidental impact is one of the main reasons why people with upper-limb amputations abandon commercially-available prosthetic hands. To address this problem, we present the design and evaluation of a compliant four-bar linkage mechanism that makes the fingers of a prosthetic hand more impact resistant. Our design replaces both the rigid input and coupler links with a monolithic compliant bone, and replaces the follower link with three layers of pre-stressed spring steel. This design behaves like a conventional four-bar linkage but adds lateral compliance and eliminates a pin joint, which is a main site of failure on impact. Results from free-end and fixed-end impact tests show that, compared to those made with a conventional four-bar linkage, fingers made with our design absorb up to 11% more energy on impact with no mechanical failure. We also show the integration of these fingers in a prosthetic hand that is low-cost, light-weight, and easy to assemble, and that has grasping performance comparable to commercially-available hands.