The present invention pertains to a remote center of motion robot for medical image scanning and image-guided targeting, hereinafter referred to as the "Euler" robot. The Euler robot allows for ultrasound scanning for 3-Dimensional (3-D) image reconstruction and enables a variety of robot-assisted image-guided procedures, such as needle biopsy, percutaneous therapy delivery, image-guided navigation, and facilitates image-fusion with other imaging modalities. The Euler robot can also be used with other handheld medical imaging probes, such as gamma cameras for nuclear imaging, or for targeted delivery of therapy such as high-intensity focused ultrasound (HIFU). 3-D ultrasound probes may also be used with the Euler robot to provide automated image-based targeting for biopsy or therapy delivery. In addition, the Euler robot enables the application of special motion-based imaging modalities, such as ultrasound elastography.