## 1 Introduction
### The Effect of Parasitic Motion on the Application of Lower Mobility Parallel Manipulators  
The applications of robotic manipulators described above require lower DoFs with higher accuracy. Thus, researchers showed keen interest in the use of PMs with lower DoFs instead of the serial ones. Even though parallel manipulators are comparatively accurate enough, a hidden property of lower mobility PMs named parasitic motion can considerably affect accuracy [12]. Parasitic motion is a small dependent movement that occur in the restricted DoFs due to the nature of constraint [12]. For the applications that require higher precision, such as machining, pointing devices, and robotic surgery, parasitic motion causes accuracy problems and control complexity [22]. Because parasitic motion is an unwanted auto-generated movement only to satisfy the structural constraint, and the internal controller cannot correct it.  
Therefore, researchers aim to describe parasitic motion, introduce methods to remove the parasitic terms, and invent manipulators without parasitic movement considering various applications sensitive to this natural behavior [12; 21; 22]. Through the extensive research carried out to define and analyze parasitic motion, [PERSON] et al. were the first to address it appropriately at the position-level [12]. Their study has also introducedthe optimal configuration of a 3-PRS manipulator that minimizes this undesired motion. Later in 2011, [PERSON] et al. [22] also investigated 3-PRS manipulator without and with small amplitude parasitic motion using different limb arrangements. In 2010, [PERSON] and [PERSON] synthesized 1T2R manipulators without parasitic motion [18]. [PERSON] et al. also introduced a method to remove the parasitic motion of 3-UPU by adding a redundant active leg [23]. A simplified method to describe the rotational parasitic motion was introduced by [PERSON] et al. in 2008 [24]. However, the proposed approach is also at the position-level.  
In this study, the optimum geometric parameters are obtained purely at the velocity level. Deriving the parasitic motion equation at the velocity level avoids unnecessary explicit position relation coverage. It also suits the commonly used velocity-level control scheme. Previously, the procedure had to start from the position-level relations. However, that is ineffective for someone who does not necessarily need the position information. Note that the parallel manipulator's control scheme is commonly based on the velocity information since the theory for the velocity analysis is well-established for such mechanisms. Also, embedding the constraint information in the position equation is not uniformly applicable for all manipulators since it is obtained differently for each mechanism. The analytic constraint equation used to formulate parasitic velocity is obtained via screw theory using instantaneous restriction and motion spaces [25; 26]. Consequently, the manipulators that optimize the parasitic velocities are obtained.  
Moreover, the paper introduces an enhanced performance manipulator without parasitic motion after the performance evaluation of optimized manipulators.