Robot manipulators can be broadly classified into open or closed depending upon the connections between each link and the end effector. Due to the open structure of serial manipulators, the errors and inertial effects in each link gets added up at the end effector which results in reduced accuracy and rigidity. A Parallel Manipulator (PM) has the end effector connected by several independent kinematic chains that enable superior rigidity and precision over serial manipulators [
1,
2]. These mechanisms have wide applications in manufacturing and service industries, health care, space, etc. PMs also have a higher payload to weight ratio since the load carried by the end effector is distributed along the legs within the mechanism. However, most parallel manipulators have lower workspace compared to serial manipulators due to the constraint motion of the end effector. Various researchers have proposed different designs of PMs having multiple Degrees of Freedom (DoF) depending upon the applications. Among these, the six DoF symmetric PMs are the most promising architecture because of its relatively larger workspace and lower singularities [
3,
4]. The Stewart-Gough platform, one of the early proposed six DoF PM, has two platforms connected via six limbs [
5,
6]. Merlet [
7] and Domagoj et al. [
8] analysed the forward and inverse kinematic equations for the Stewart-Gough mechanism using interval analysis method and geometrical approach respectively. David et al. [
9] have proposed another six DoF parallel mechanism for accurate measurement applications. The direct kinematics for the mechanism is obtained using the geometrical approach, and the design parameter optimization is based on the study of the condition number of the Jacobian. Nicholas et al. [
10] introduced a six DoF PM having six legs. It consists of three prismatic actuators each aligned parallel to one axis of the cartesian plane. Each leg consists of two passive revolute joints whose axis is parallel to the direction of the prismatic joint. Each leg is attached to the mobile platform via a spherical joint. The direct kinematics for the mechanism is solved by considering the orientation and the position separately in the mathematical model. However, the orientations of the mobile platform is limited due to the interferences between the legs during motion making it difficult for applications needing higher mobility. Byun et al. [
11] have developed the 3-
PPSP parallel manipulator also having six DoF. The solutions for the inverse and forward kinematics are obtained from the geometrical model, and the workspace is computed by applying suitable displacements to each active prismatic joint. Bruno et al. [
12] proposed an optimal design for a six DoF parallel mechanism having three legs. The mechanism consists of a mobile platform connected to the base by three identical five-bar linkages. The workspace analysis is done using the geometrical kinematic model, and its optimisation is done to ensure maximum singularity free constant orientation workspace. Ketankumar et al. [
13] developed the loop closure equations for the planar 3-
RRR PM and analyzed the singularity using Instantaneous Centre of Rotation (ICR) method. This methodology is however applicable to simple architectures and difficult for spatial mechanisms. Singularity is an inherent property of closed chain mechanisms which occurs when the motion of the end effector does not produce any motion of the end effector or when the end effector cannot resist any forces or torques even if all actuators are locked. Gabardi et al. [
14] have presented the complete kinematics of a 4-U
PU parallel manipulator by Screw Theory, and further, the Jacobian Singularities have been determined. A numerical procedure for optimizing the geometrical parameters to get a singularity-free workspace is also presented in the paper. Refs. [
15] and [
16] are other examples of analytical parallel kinematics solution via Screw theory whose design has been optimized by considering the singularity-free workspace. One common solution to avoiding singularities within the workspace is by replacing one or more passive joints with actuated joints. Sreenivasan et al. [
17], Hunt and Primrose [
18] and Bruyninckx [
19] proposed parallel mechanisms having six joints each on the base and the mobile platform. These mechanisms possess higher stiffness, lower inertia effects and larger payload carrying capacities. However, these mechanisms have relatively lower work volumes with complex architecture. Obtaining the direct kinematics for these mechanisms from the conventional geometrical approach or Screw theory is a difficult task. Serder [
20] has demonstrated the application of modified DH modelling technique to obtain the kinematic relations for the planar 3 DoF
RRR mechanism. The author has incorporated the constraints into the model by assuming appropriate constraint equations. The constant distance between any two consecutive joints on the mobile platform is considered as the constraint equation for the
RRR mechanism. By this methodology, both the passive and active joint variables are incorporated into the mathematical model. In context to real-time control, dynamics of a parallel manipulator is analysed to determine the input force to be exerted by actuators to produce a desired trajectory for the end effector. Several methods such as Euler-Lagrangian formulation [
21], Principle of Virtual Work [
22], Newton-Euler formulation [
23] are used to obtain the dynamic equations of robotic systems. Inverse dynamic analysis of a parallel mechanism is done for a pre-defined path of the end effector. Leroy et al. [
24] developed the dynamic model of a three DoF parallel mechanism by incorporating the holonomic constraints using Lagrangian multipliers into the Euler-Lagrangian equation.
Despite extensive researches happening in the field of parallel mechanisms, most mechanisms have limited workspace, complicated architecture, difficulties in solving inverse kinematics, etc. To overcome these shortcomings, the development of parallel manipulators with simpler architectures has been accelerated. Nevertheless, manipulators having decoupled motion of the end effector is quite limited and remains a challenging task especially in cases of six DoF manipulators. Geometric modelling or Screw theory are the usual approaches employed to obtain the kinematic model of parallel mechanisms. In Geometric modelling approach, the loop closure equations are formulated for the mechanism in terms of all joint variables and dimensional parameters. However, the formulation of loop closure equations is a very cumbersome task, especially for complex geometries. In addition, the procedures used in this approach cannot be generalised for all manipulator designs [
25]. Also, obtaining the loop closure equations for mechanisms having more number of legs is very difficult. Screw Theory [
14,
16,
26] is another well-established methodology which is found in many literatures to obtain the kinematic model for parallel mechanisms. According to this method, it has only two coordinate frames of which one is located at the base and the other is at the end-effector. However, in the DH modelling approach, frames are assigned to all joints up to the end effector. Therefore, the Kinematic model formulated using the DH approach will include all joint variables inclusive of both active and passive joints. Even though the computation involved with the DH model is slightly higher, the singularity analysis performed with the DH model will be more effective than that obtained from the Screw theory model. This is because the analysis considers the singularity induced due to both active and passive joints. In this paper, the authors’ have showcased a methodology to use modified DH modelling technique to reduce the computational difficulties by breaking down the closed parallel mechanism into individual serial manipulators. The conventional DH modelling is applied on each leg and finally coupled together using suitable constraint equations. Denavit-Hartenberg (DH) modelling technique is a widely used method to obtain kinematics of serial manipulators. This method is a direct and easy to learn approach for obtaining forward and inverse kinematics of open-chain mechanisms. In this paper, a novel 3-
PRUS manipulator is proposed. This mechanism has only three legs unlike the case of other 6 DoF mechanisms having six legs. This helps in reducing the inertia effects especially during fast motions. The DH modelling approach is used to investigate the kinematics of the 3-
PRUS mechanism by considering each leg as an open-chain separately. The three legs modelled separately are coupled finally using suitable constraints to account for the closed configuration of the manipulator. The conceptual design and analysis of the proposed 3-
PRUS parallel mechanism having decoupled non-redundant motions of the end effector are explained in the following sections. The conceptual design and mobility analysis of the 3-
PRUS mechanism is described in Section
2. The forward and inverse kinematics modelling is addressed in Section
3. Jacobian matrix for the manipulator is derived analytically and further used to analyse performances including singularity and stiffness indices for the manipulator. An algorithm is explained to obtain the maximum singularity free work volume for the robotic system. In Section
4, the closed form dynamic model is developed analytically using the Euler-Lagrangian formulation and compared with ADAMS results for a pre-defined trajectory path of the end effector. The results obtained are explained in Section
5. In Section
6, the details regarding the prototype manufactured is explained and analysed.