A pivotless compliant structure is disclosed that can be used to increase the geometric advantage or mechanical advantage of a microelectromechanical (MEM) actuator such as an electrostatic comb actuator, a capacitive-plate electrostatic actuator, or a thermal actuator. The compliant structure, based on a combination of interconnected flexible beams and cross-beams formed of one or more layers of polysilicon or silicon nitride, can provide a geometric advantage of from about 5:1 to about 60:1 to multiply a 0.25-3 .mu.m displacement provided by a short-stroke actuator so that such an actuator can be used to generate a displacement stroke of about 10-34 .mu.m to operate a ratchet-driven MEM device or a microengine. The compliant structure has less play than conventional displacement-multiplying devices based on lever arms and pivoting joints, and is expected to be more reliable than such devices. The compliant structure and an associated electrostatic or thermal actuator can be formed on a common substrate (e.g. silicon) using surface micromachining.