Context : Many aspects of massive star ( \ga 10 M _ { \odot } ) formation are still unclear .
In particular , the outflow properties at close distance ( 100–1000 AU ) from a “ Massive Young Stellar Object ” ( MYSO ) are not yet well established .

Aims : This work presents a detailed study of the gas kinematics towards the “ Hot Molecular Core ” ( HMC ) G31.41 + 0.31 .

Methods : To study the HMC 3-D kinematics at milli-arcsecond angular resolution , we have performed multi-epoch VLBI observations of the H _ { 2 } O 22 GHz and CH _ { 3 } OH 6.7 GHz masers , and single-epoch VLBI of the OH 1.6 GHz masers .

Results : Water masers present a symmetric spatial distribution with respect to the HMC center , where two nearby ( 0 \aas@@fstack { \prime \prime } 2 apart ) , compact , VLA sources ( labeled “ A ” and “ B ” ) are previously detected .
The spatial distribution of a first group of water masers , named “ J1 ” , is well fit with an elliptical profile , and the maser proper motions mainly diverge from the ellipse center , with average speed of 36 km s ^ { -1 } .
These findings strongly suggest that the “ J1 ” water maser group traces the heads of a young ( dynamical time of 1.3 10 ^ { 3 } yr ) , powerful ( momentum rate of \simeq 0.2 M _ { \odot } yr ^ { -1 } km s ^ { -1 } ) , collimated ( semi-opening angle \simeq 10 ° ) jet emerging from a MYSO located close ( within \approx 0 \aas@@fstack { \prime \prime } 15 ) to the VLA source “ B ” .
Most of the water features not belonging to “ J1 ” present an elongated ( \approx 2″ in size ) , NE–SW oriented ( PA \approx 70° ) , S-shape distribution , which we denote with the label “ J2 ” .
The elongated distribution of the “ J2 ” group and the direction of motion , approximately parallel to the direction of elongation , of most “ J2 ” water masers suggests the presence of another collimated outflow , emitted from a MYSO placed near the VLA source “ A ” .
The proper motions of the CH _ { 3 } OH 6.7 GHz masers , mostly diverging from the HMC center , also witness the expansion of the HMC gas driven by the “ J1 ” and “ J2 ” jets .
The orientation ( PA \approx 70° ) of the “ J2 ” jet agrees well with that ( PA = 68° ) of the well-defined V _ { LSR } gradient across the HMC revealed by previous interferometric , thermal line observations .
Furthermore , the “ J2 ” jet is powerful enough to sustain the large momentum rate , 0.3 M _ { \odot } yr ^ { -1 } km s ^ { -1 } , estimated from the interferometric , molecular line data in the assumption that the V _ { LSR } gradient represents a collimated outflow .
These two facts lead us to favour the interpretation of the V _ { LSR } gradient across the G31.41 + 0.31 HMC in terms of a compact and collimated outflow .

Conclusions :