To make constrained manipulation of 3D objects in desktop 3D applications, 3D transformation widgets are commonly used. However, their performance degrades on touchscreens because of low accuracy of touch inputs and the fingertip occlusion problem. In this paper, we present TouchSketch, a touch-based interface which allows users to perform independently fine-grained object translation, rotation and scaling on mobile devices. Our manipulation technique permits using the non-dominant hand to specify the manipulation reference while the dominant hand is used to determine the operation mode and control the transformation. In addition to 3D manipulation, TouchSketch provides also a set of functions to edit the shape of 3D objects. Users can use this application to accomplish rapid sketching tasks. We have conducted a user study to evaluate the efficiency of our manipulation technique. The results show that our technique outperforms a Widget-based technique regarding both the efficiency and fluency.