## 1 Introduction  
In recent years, the deployment of lower DoF mechanisms has grabbed the attention of industries and academia due to its interesting properties such as lower cost, kinematic simplicity, fast dynamic response and higher accuracy. For several applications, such as pointing devices, surgical robots, parallel kinematic machines (PKMs), parallel manipulators (PMs) with less than six DoFs can be preferable [1, 2, 3, 4, 5]. Because such tasks can be well performed with manipulators having less than 6-DoFs. For example, surgical devices require 4 DoFs at most including one external yaw motion of the tool [6]. Lower mobility PMs as a pointing device:Replacing conventional antenna and telescope positioning methods with PMs dates back to 1980 when first suggested by [PERSON] and [PERSON] and later continued by [PERSON] at the Canterbury University [7]. Pointing devices often operate in a complex environment that could heavily affect their accuracy, such as telescopes on satellite continuously changes its pose in relation to the telescope mounted on the ground. However, these devices require higher accuracy and precision to guarantee strong signals in tracking and communication. To ensure the pointing precision under complex operational environment, engineers employed 6-DoFs PM instead of the conventional mounting methods [8; 9; 10]. [PERSON] et al. introduced a new 6-PSS (prismatic-spherical-spherical) telescope's secondary mirror alignment mechanism [8]. [PERSON] et al. proposed another 6-DoFs hybrid manipulator for pointing and positioning purposes in aerospace applications [11]. However, manipulation of the secondary mirror of the telescope requires 3-DoFs at most [12]. The remaining degrees of freedom of the manipulator are to avoid singularities. But singularity can be handled by PMs with less than 6-DoFs [12; 13]. To avoid the use of such complicated manipulators for lower DoFs tasks, researchers shifted their attention to fewer DoFs mechanisms. [PERSON] et al. designed a 3-PRS (prismatic-revolute-spherical) manipulator to perform tip/tilt pointing (2 rotational freedoms) and focusing (1 translational freedom) for the secondary mirrors of a Cassegrain telescope [12]. In 2008, a 3-PRS PM was proposed for orienting television satellite antenna [14]. Likewise, the high-performance antenna pointing device (3 POD) in a micro-gravity environment was proposed by CENS [13]. Lower mobility PMs as high precision PKMs: PKMs use their actuators working side-by-side to enhance rigidity, fast dynamic response, and accuracy. Due to these advantages, the interest has increased both in academia and industry to use lower mobility PMs as a machining device. The first PKM was introduced at the international machine tool show (IMPS) in 1994. Along that track, there have been intensive research and innovations to meet the conceptual potentials of PKMs [15; 16; 17; 18]. In 2016, the most successful sprint Z3 [19] of the Eospeed series from Starrag Group had received significant orders in the double-digit million from customers. This success indicates the Eospeed series with sprint Z3-head has become a choice to achieve 5-axis precision machining in spacecraft and automobile industries. Inspired by Z3-head, Tianjin university developed a PKM with identical motion but with RPS(Revolute-Prismatic-Spherical) joint arrangements in a limb [18]. Both manipulators are extensively studied and are the most used examples to demonstrate different theoretical and experimental approaches. Lower mobility PMs as surgical devices: One of the medical industry's growing trends is to use robotic-assisted surgery to take advantage of parallel manipulators' high accuracy and accessibility. Robots in the medical sector can help surgeons handle routine tasks, complement their skills with manipulators' accuracy and repeatability, and several researchers focused on exploring PMs' capabilities in medical applications.