In the field of robotic hands, finger force coordination is usually achieved by complex mechanical structures and control systems. This study presents the design of a novel transmission system inspired from the physiological concept of force synergies, aiming to simplify the control of multifingered robotic hands. To this end, we collected human finger force data during six isometric grasping tasks, and force synergies (i.e. the synergy weightings and the corresponding activation coefficients) were extracted from the concatenated force data to explore their potential for force modulation. We then implemented two force synergies with a cable-driven transmission mechanism consisting of two spring-loaded sliders and five V-shaped bars. Specifically, we used fixed synergy weightings to determine the stiffness of the compression springs, and the displacements of sliders were determined by time-varying activation coefficients. The derived transmission system was then used to drive a five-finger robotic hand named SYN hand. We also designed a motion encoder to selectively activate desired fingers, making it possible for two motors to empower a variety of hand postures. Experiments on the prototype demonstrate successful grasp of a wide range of objects in everyday life, and the finger force distribution of SYN hand can approximate that of human hand during six typical tasks. To our best knowledge, this study shows the first attempt to mechanically implement force synergies for finger force modulation in a robotic hand. In comparison to state-of-the-art robotic hands with similar functionality, the proposed hand can distribute humanlike force ratios on the fingers by simple position control, rather than resorting to additional force sensors or complex control strategies. The outcome of this study may provide alternatives for the design of novel anthropomorphic robotic hands, and thus show application prospects in the field of hand prostheses and exoskeletons.