Recalibrating Home-position
When homing the printer, the hot end carriage will be instructed to hit the (mechanical or optical) end stops. From this point a well configured firmware knows where to find the origin of the heat bed. 

For the printer to know the origin of the bed, offsets are defined in the firmware from the end stop locations to the actual origin of the heat bed. 

E.g. in Marlin Firmware this is defined by

 #define X_MIN_POS -35 ; move the head 35 mm to the right to place the 
                       ; nozzle at X = 0
 #define Y_MIN_POS -8  ; move the head 8 mm to the back (or the plate
                       ; forward) to place the nozzle at Y = 0


When you change the hardware (e.g. carriage), you need to re-calibrate the movement from the end stop location to the origin of the bed. Note that any arbitrary point on the heat bed can be used to re-calibrate this. E.g. the center of the bed can also be used, and is frequently much more easy to re-calibrate as the heated beds usually have rounded corners or are slightly larger than the actual print area (e.g. I have a 300 x 300 mm heat bed that actually measures 315 x 315 mm). Printing a large square on the heat bed will therefore give you a good impression of the offset of the nozzle due to your new carriage design. 

Note that, if you cannot or will not flash new firmware, an alternative solution exists to set new incremental offset values using the M206 command IF your current firmware supports this.

A detailed description to re-calibrate is found in answer How to center my prints on the build platform? or in external link Bed center calibration.