[ulis], 2004-01-29. No, Tcl nor Tk can move your mouse or your hand. But Tk (with the help of Tcl) can move the mouse cursor on your screen.
The trick is to use the '''-warp''' option of the '''event generate''' command. (This trick comes from [Kroc]).

A little script to illustrate this:

  pack [button .b -text Ok -width 4 -command exit]
  bind . <Key> { set ::stop 1 }
  update
  set stop 0
  set x -20; set y -10; set incrx 1; set incry 0.5
  proc move {} \
  {
    if {$::stop} { return }
    set ::x [expr {$::x + $::incrx}]
    set ::y [expr {$::y + $::incry}]
    if {$::x < 20} \
    { 
      event generate .b <Motion> -warp 1 -x $::x -y $::y
      after 100 move 
    } \
    else \
    { 
      event generate .b <ButtonPress-1>
      after 100 event generate .b <ButtonRelease-1>
    }
  }
  focus -f .
  raise .
  move

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'''See also'''

   * This is covered in [warp]
   * An alternative on Windows NT and above is the move_mouse command that is part of [TWAPI]

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[APN] The above script didn't seem to do anything as far as I could tell on my Win2K box. Also, is warping restricted to Tk windows only or can the mouse be moved anywhere on the screen (for automation tests for example). An alternative on Windows NT and above is the move_mouse command that is part of [TWAPI].

[ulis] Very surprising: I tested it on a W2k box. Maybe Tk version matters: I used 8.4. 

The x & y coords are computed for the Tk widget (.b here) and the cursor can go outside the widget.

Under good conditions the script move the cursor mouse from outside the widget to the center of the button.

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[LV] as a user, just let me say how much I hate the fact that right now, the
[GNOME] metacity window manager moves the mouse around to windows that it
thinks should get focus.  There I will be, typing away, when all of a sudden
the mouse warps over to Netscape or some other window, and my keystrokes,
at best, are ignored, and at worst, cause things like screens to lock,
or forms to be submitted, or whatever.

'''PLEASE BE JUDICIOUS IN YOUR USE OF THIS TECHNIQUE!!!'''' 
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[Don't do that] has more discussion.
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[JPT] Using the DLL extension under Windows, one can move and click the mouse with a proc like this one:

  set MOUSEEVENTF_LEFTUP 0x4 
  set MOUSEEVENTF_LEFTDOWN 0x2

  proc MouseClick {x y} {
    ::dll::call user32 SetCursorPos i "i $x" "i $y"
    ::dll::call user32 mouse_event i "i $::MOUSEEVENTF_LEFTDOWN" {i 0} {i 0} {i 0} {i 0}
    ::dll::call user32 mouse_event i "i $::MOUSEEVENTF_LEFTUP" {i 0} {i 0} {i 0} {i 0}
  }

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[Category GUI]
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'''[SeS] - 2012-04-03 10:42:08'''
The information in this page inspired me to implement a little proc into [tG²] v1.06.0.34 when layouts forms/toplevels are opened, to set the position of the mouse pointer to the center of the layout-toplevel.  

======
proc centerMouse2 {w {wmgeo ""}} {
  if {$wmgeo==""} {set wmgeo [winfo geom $w]}
  set t [split [split $wmgeo x] +]
  event generate $w <Motion> -warp 1 -x [expr [lindex $t 0 0]/2] -y [expr [lindex $t 0 1]/2]
}
======

usage: 
  centerMouse2 <toplevel path> ?geometry of the toplevel?