I was standing still on a platform ladder when shooting this photo, so not in motion. However, I have several other examples of posed photos like this where only the right side of the photo is blurred. At first I thought it was the camera, then the lens, but I have noticed this in photos shot with all three (Nikon D5000, D500, D750) of my cameras using four different lenses (2 different Tamron 18-270's, Tamron 18-400, and Tamron 150-600). So it has to be user error (me) rather than equipment error.
If it's happening with three different cameras and four different lenses, then it's almost certainly attributable to shooting technique. My guess is that the way you are pressing the shutter button tends to cause the camera to rotate slightly around an axis to the upper left of the camera, thus blurring the lower right portion of photos. (Think of a picture frame nailed to the wall at the upper left corner. When the picture is rotated around the nail, the lower right corner will move further for each degree of movement than any other part of the picture, with the upper left moving the least.)
The only other remote possibilities are that all of your lenses, which are wide-range zooms of less than stellar quality, have slightly misaligned lens elements that affect the same area of the image or that all of your cameras have sensor-lens flange alignment issues in the same direction. I guess the latter might be attributable to some way in which all of your cameras with relatively long lenses may have been stressed in such a way that all of the flange rings have been tweaked in the same direction. But the possibilities of either of these seem highly unlikely to me.
Try putting your camera on a sturdy tripod and releasing the shutter with a wired or cable remote or by using the 10-second timer. If outdoors, do the testing when there is little or no wind. This should reveal if there are mechanical issues with your gear.
Try putting the camera in burst mode and take several series of 3-4 frames holding the shutter button down. If the problem is in the way you're holding the camera and pressing the shutter, the first frame will tend to be the blurriest. You can also compare the composition of each successive frame to see if the camera is being held stead or moving in any way, whether rotating or panning.