This paper proposes a new type of hybrid manipulator that can be of extensive use in industries where translational motion is required while maintaining an arbitrary end-effector orientation. It consists of two serially connected parallel mechanisms, each having three degrees of freedom, of which the upper platform performs a pure translational motion with respect to the mid-platform. Closed-form forward and inverse kinematic analysis of the proposed manipulator has been carried out. It is followed by the determination of all of its singular configurations. The theoretical results have been verified numerically, and the 3D modeling and simulation of the manipulator have also been performed. A simple optimal design is presented based on optimizing the kinematic manipulability, which further demonstrates the potential of the proposed hybrid manipulator.

In order to resolve redundancy and path planning of a high DOF mobile manipulator using conventional approaches like Jacobian and a pseudoinverse method, researchers face the limitation of computational load and delay in response. If such kind of mobile manipulator is traversing the rough terrain, then conventional methods become too costly to implement due to the handling of redundant joints, obstacles, and wheel-terrain interaction. A few optimization-based redundancy resolution approaches try incorporating wheel-terrain interaction but fail in real-time response. This paper describes a 14 DOF Rover Manipulator System’s end-effector path-tracking approach using CG-Space framework to incorporate wheel-terrain interaction. CG-Space means the center of gravity (CG) locus of the Rover. The Rover’s CG is calculated while traversing over 3D terrain using a multivariable optimization method and a 3D point cloud image of the actual terrain and stored as CG-Space over the given terrain. First of all, we decide which part of the system moves to track the path, that is, arm or Rover, depending upon the manipulator’s work volume and manipulability measure restrictions. The next task is to obtain the Rover pose according to the end-effector path using a simple arm’s inverse kinematic solution between the CG-Space and end-effector task space without resolving redundancy. Meanwhile, obstacles and non-traversable regions are avoided in CG-Space. On diverse 3D terrains, simulation and experimental results support the suggested CG-Space framework for end-effector tracking.

This paper presents a comprehensive study of the forward and inverse kinematics of a six-degrees-of-freedom (DoF) spatial manipulator with a novel architecture. Developed by Systemantics India Pvt. Ltd., Bangalore, and designated as the H6A (i.e., Hybrid 6-Axis), this manipulator consists of two arm-like branches, which are attached to a rigid waist at the proximal end and are coupled together via a wrist assembly at the other. Kinematics of the manipulator is challenging due to the presence of two multi-DoF passive joints: a spherical joint in the right arm and a universal in the left. The forward kinematic problem has eight solutions, which are derived analytically in the closed form. The inverse kinematic problem leads to $160$ solutions and involves the derivation of a $40$-degree polynomial equation, whose coefficients are obtained as closed-form symbolic expressions of the pose parameters of the end-effector, thus ensuring the generality of the results over all possible inputs. Furthermore, the analyses performed lead naturally to the conditions for various singularities involved, including certain non-trivial architecture singularities. The results are illustrated via numerical examples which are validated extensively.

Robot-assisted minimally invasive surgery (MIS) has shown tremendous advances over the traditional technique. A crucial challenge for developing a MIS robot is the kinematic design of the remote center-of-motion (RCM) mechanism. In this paper, a class of spatial RCM mechanism is analyzed. They are obtained by generating virtual parallelograms. The main process is to construct a line that passes through a fixed point under the mechanical constraint. The axis of the surgical tool is then constrained to parallel with that line. Hence, due to the geometrical feature of the parallel lines, the axis of the surgical tool will always pass through a fixed point, i.e., the RCM point. Due to the specially designed structure, the fixed point does not need to be physically belonging to the mechanism. The geometrical analysis method is employed to obtain the closed-form solution of the forward kinematics of the proposed mechanisms. Due to the high load capacity of parallel mechanism, the robots based on the proposed RCM mechanisms have promising applications as an external positioner to be used in robotic single-port surgeries.

In the current research, kinematic analysis of a humanoid NAO is attempted. Here, both Denavit–Hartenberg (DH) parameter approach and multibody formulation approach have been analyzed. In the DH parameter approach, the NAO robot is solved by separating it into five individual kinematic chains. In the multibody formulation approach, NAO is divided into 15 segments, and each segment is analyzed. Kinematic analysis holds a significant importance; as from the data obtained in the kinematic analysis, the robots can be designed for real-time path planning and navigation. The current analysis is a novel approach to analyze the NAO based on its kinematic constraints.

Forward kinematics is essential in robot control. Its resolution remains a challenge for continuum manipulators because of their inherent flexibility. Learning-based approaches allow obtaining accurate models. However, they suffer from the explosion of the learning database that wears down the manipulator during data collection. This paper proposes an approach that combines the model and learning-based approaches. The learning database is derived from analytical equations to prevent the robot from operating for long periods. The database obtained is handled using Deep Neural Networks (DNNs). The Compact Bionic Handling robot serves as an experimental platform. The comparison with existing approaches gives satisfaction.

This paper addresses the application of a novel elimination algorithm with a newly developed homotopy continuation method (HCM) for forward kinematics of a specific hybrid modular manipulator known as n-(6UPS). First, the kinematic model of n-(6UPS) was extracted using a homogenous transformation matrix method. Then, a novel algebraic elimination algorithm was developed to transform the highly nonlinear proposed kinematic model into a system of polynomial equations for each module. Next, the HCM is considered to solve the system of equations. Comparison of the results from the proposed approach with experimental data and other methods demonstrates the efficiency of the proposed contribution.

In order to solve general kinematics modeling problems and numerical stability problems of numerical methods for spatial parallel linkage mechanisms, a general modeling method and its numerical solving algorithm is proposed. According to the need for avoiding direct singular configurations, valid joint variable space and valid forward kinematics solutions (VKSs) are defined. Taking numerical convergence near singular points into account, the pseudo-arc length homotopy continuation algorithm is given to solve the kinematics model. Finally as an example, the joint variable space of the general Stewart platform mechanism is analyzed, which is proved to be divided into subspaces by direct singular surfaces. And then, forward kinematics solutions of 200 testing points are solved separately using the pseudo-arc length homotopy continuation algorithm, the Newton homotopy continuation algorithm and the Newton–Raphson algorithm (NRA). Comparison of the results shows that the proposed method is convergent to the same solution branch with the initial configuration on all the testing points, while the other two algorithms skip to other solution branches on some near singular testing points.

In this paper, a fast and efficient evolutional algorithm, called the G3-PCX has been implemented to solve the forward kinematics problem (FKP) of the general parallel manipulators being modeled by the 6-6 hexapod, constituted by a fixed and mobile platforms being non planar and non-symmetrical. The two platforms are connected by six linear actuators, each of which is located between one ball joint and one universal joint. Forward kinematics are formulated using Inverse Kinematics applying one position based equation system which is converted into an objective function by expressing the sum of squared error on kinematics chain lengths and mobile platform distances. In less than one second, the 16 unique real solutions are computed with improved accuracy when compared to previous methods.

This paper introduces the design and kinematic analysis of a 5-DOF (multiple degree of freedom) hybrid-driven MR (Magnetic Resonance) compatible robot for prostate brachytherapy. It can slip the leash of template and rely on the high precise of MR imaging. After a brief introduction on design requirements of MR compatible robot, a description of our robot structure, material selection, hybrid-driven, and control architecture are presented. Secondly, the forward kinematics equations are obtained according to the equivalent diagram of this robot, and the actual workspace can be outlined. This will help the designer to determine whether this robot can be operated in the MR core without intervention with patient. And then, the inverse kinematics equations combined with trajectory planning are used to calculate the actuators movement. This will help the control system to manipulate the robotic accurately. Finally, vision based experiments on phantoms are used to verify the mechanism precision. As the results shown, the needle tip precision of mechanism is 0.9 mm in the general lab environment.

Contrary to the inverse kinematics, the forward kinematics of parallel manipulators involves solving highly non-linear equations and provides more than one feasible end-effector pose, which are called the assembly modes, for a given set of link lengths or joint angles. Out of the multiple feasible solutions, only one solution can be achieved from a certain initial configuration. Therefore, in this paper, the Kohonen's self-organizing map (SOM) is proposed to learn and classify the multiple solution branches of the forward kinematics and then provide a unique real-time solution among the assembly modes. Each solution of the multiple feasible ones is coded using IF-THEN rules based on the values of the passive joint variables. Due to not only the classification but also the associative memory learning abilities of the SOM, the passive joint variables vector, the end-effector pose vector, and this class code are associated with the active joint variables vector constituting the input vector to the SOM in the offline learning phase. In the online testing phase, only the active joint variables vector and the class code are fed to the SOM to obtain the unique end-effector pose vector. The Jacobian matrix calculated at the SOM output layer is used for further fine tuning this output to obtain an accurate end-effector pose vector. Simulations are conducted for 3-RPR and 3-RRR planar parallel manipulators to evaluate the performance of the proposed method. The results proved high accuracy of the desired unique solution in real-time.

Hybrid robots, composed of a parallel platform and serial wrist, achieve a compromise of stiffness and dexterity. Thus, they are well suited for applications such as aircraft component machining and automotive assembly, where high accuracy and large workspace movements are required. However, their forward kinematics can be highly coupled and be nonlinear. To reduce the time required to define the forward kinematics of a robot with parallel–serial structure, this paper introduces the use of neural networks. Two radial basis function networks are trained to learn the parallel and serial kinematics separately, and then integrated into a complete model. The error of this network model is analyzed and identified by a particle swarm optimization algorithm. Simulation and experiment results are obtained from the hybrid robot, Exechon, which shows that the developed kinematic model is able to produce accurate position and orientation estimates of the end-effector. The computation time of the neural network model is greatly reduced when compared to the time achieved by the numerical model.

This paper presents a simple numerical method for forward kinematics of general Stewart–Gough platforms, which can generate a unique solution directly. This method utilizes the trivial nature of the inverse kinematics of parallel manipulators, and derives a straightforward linear relationship between the small change in joint variables (leg lengths) and the resulting small motion of the platform. The solution to the forward kinematics is then achieved through a series of small changes in joint variables. Numerical examples validate and confirm the efficiency of the method.

In this paper, a 3-DOF parallel kinematic machine (PKM) with a passive link is introduced. The forward kinemaic model is established, and a new technique is proposed to solve this model. The developed forward kinematic solver (FKS) is employed in two new applications: the determination of joint workspace and sensor-based real-time monitoring. A joint workspace concept is proposed for the optimization of a PKM structure. It is defined as a reachable area in the joint coordinate system under given ranges of active joint motions. The larger a joint workspace is, the higher utilization of joint motion capacity is. Sensor-based monitoring is applied in real-time system operation, by which a remote user can monitor a PKM through Internet based on the feedbacks of the joint encoders or the on-site stereo camera.

In this paper, the joint angles of a two link planar manipulator are calculated by using inverse kinematics equations together with some geometric equalities. For a given position of the end-effector the joint angle and angular velocity of the links are derived. The analyses contains many equations which have to be solved. However, the solutions are rather cumbersome and complicated, therefore a program is written in Fortran 90 in order to do, the whole calculation and data collection. The results are given at the end of this paper.