BLTouch missing build plate on levelling

Tiny Machines firmware is based on Marlin firmware. Note that I personally am more comfortable using the original sources than a fork or copy from another derivative source. Using a derivative means that you will have to wait a second development commitment to post new features and bug fixes.

A similar reasoning is applicable using premade hex files opposed to compiling the sources yourself.

There are 2 things (related to the bed X, Y positioning) you need to be aware of when using a Z probe. When using the probe you must ensure that the probe deploys on the bed during probing.

First, define in your firmware that the probe can only deploy in the center of the build plate. In e.g. Marlin firmware this is described in the configuration.h; you need to enable Z_SAFE_HOMING:

// Use "Z Safe Homing" to avoid homing with a Z probe outside the bed area.
//
#define Z_SAFE_HOMING

Second, you need to define a confined bed area for the sensor to deploy, this is described in question: "How to set Z-probe boundary limits in firmware when using automatic bed leveling?".

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Note that flashing an existing firmware does not guarantee anything, the used firmware from Tiny Machines (or e.g. from TH3D) try to simplify the firmware configuration for you by adding additional specific settings/constants (#defines), underneath the waterline all sorts of things are then handled for you. Personally I'd like to be in control and do the modifications myself. If the probe position you use is different from the probe position used in the pre-build firmware you will not be able to use this firmware safely. We can check this: e.g. in the Tiny Machines firmware there are 3 predefined positions for the sensor, in the sources itself none is active (see below), so it is not known which option is used for compiling the hex files they made available:

//#define CREALITY_ABL_MOUNT //Using creality ABL mount
//#define E3D_DUALFAN_MOUNT // Using HD Modular mount as above with 2 5015 blowers and sensor on the right
//#define E3D_PROBEMOUNT_LEFT // Default is probe mounted to the right for E3D. Set this to invert.

When you define one of these options above, the probe position can be read from:

   #if (ANY(ABL_BLTOUCH, ABL_EZABL,ABL_NCSW) && ANY(HotendE3D, HotendMosquito))
    #if ENABLED(E3D_DUALFAN_MOUNT)
      #if ENABLED(E3D_PROBEMOUNT_LEFT)
        #define NOZZLE_TO_PROBE_OFFSET { -63, 5, 0 }
      #else
        #define NOZZLE_TO_PROBE_OFFSET { 63, 5, 0 }
      #endif
    #else
      #define NOZZLE_TO_PROBE_OFFSET { 32, 5, 0 }
    #endif
   #endif

You will see that the E3D_PROBEMOUNT_LEFT and E3D_DUALFAN_MOUNT need to be active (you see that E3D_PROBEMOUNT_LEFT is embedded in the E3D_DUALFAN_MOUNT option, this cannot be correct...) to get a probe offset of (-63, +5) which is close to your probe (60 mm to the left and 6 mm forward translates to (-60, +6)). This is exactly why I use the Marlin firmware from the main source code, not a simplified derivative (which in this case is not accurate and unknown what options are used in the pre-build hex files).

Please note that the original Marlin sources also maintain configuration files for many printer types, e.g. the CR-10S is also listed in this overview.