We report proper motion measurements of water masers in the massive-star forming region W 51A and the analyses of the 3-D kinematics of the masers in three maser clusters of W51A ( W51 North , Main , and South ) .
In W 51 North , we found a clear expanding flow that has an expansion velocity of \sim 70 km s ^ { -1 } and indicates deceleration .
The originating point of the flow coincides within 0 \arcsec .1 with a silicon-monoxide maser source near the HII region W 51d .
In W51 Main , no systematic motion was found in the whole velocity range ( 158 km s ^ { -1 } \leq V _ { \mbox { \scriptsize LSR } } < - 58 km s ^ { -1 } ) although a stream motion was reported previously in a limited range of the Doppler velocity ( 54 km s ^ { -1 } \leq V _ { \mbox { \scriptsize LSR } } < 68 km s ^ { -1 } ) .
Multiple driving sources of outflows are thought to explain the kinematics of W51 Main .
In W51 South , an expansion motion like a bipolar flow was marginally visible .
Analyses based on diagonalization of the variance-covariance matrix of maser velocity vectors demonstrate that the maser kinematics in W 51 North and Main are significantly tri-axially asymmetric .
We estimated a distance to W51 North to be 6.1 \pm 1.3 kpc on the basis of the model fitting method adopting a radially expanding flow .