Working Space and Motion Analysis on a Novel Planar Parallel Manipulator with Three Driving Sliders

The objective of this paper is to determine whether a planar parallel manipulator with redundant actuation has better tracking accuracy than a planar parallel manipulator without redundant actuation. The effects of the redundant actuation on tracking accuracy of parallel manipulators are studied by using two different experimental platforms. The first platform is the planar five-bar parallel manipulator with normal actuation, and the other one is the planar parallel manipulator with redundant actuation. The dexterity pictures and the kinematic configurations of the two platforms validate the kinematic advantages from the redundant actuation. In order to study the dynamic advantages of the redundant actuation further, a nonlinear adaptive controller is presented for the two platforms. The experimental comparison is implemented on two actual parallel manipulator platforms, and from the experimental results, one can find the tracking accuracy of the parallel manipulator with redundant actuation can be improved above 38% than that of the five-bar parallel manipulator without redundant actuation.

In the design of a mechanism, the quality of effort transmission is a key issue. Traditionally, the effort transmissivity of a mechanism is defined as the quantitative measure of the power flowing effectiveness from the input link(s) to the output link(s). Many researchers have focused their work on the study of the effort transmission in mechanisms and diverse indices have been defined. However, the developed indices have exclusively dealt with the studies of the ratio between the input and output powers and they do not seem to have been devoted to the studies of the admissible reactions in passive joints. However, the observations show that it is possible for a mechanism to reach positions in which the transmission indices will have admissible values but the reaction(s) in passive joint(s) can reach excessively high values leading to the breakdown of the mechanism. In the present paper, a method is developed to ensure the admissible values of reactions in passive joints of planar parallel manipulators. It is shown that the increase of reactions in passive joints of a planar parallel manipulator depends not only on the transmission angle but also on the position of the instantaneous center of rotation of the platform. It allows the determination of the maximal reachable workspace of planar parallel manipulators taking into account the admissible reactions in its passive joints. The suggested method is illustrated via a 5R planar parallel mechanism and a planar 3-RPR parallel manipulator.

The aim of this paper is to characterize the notion of aspect in the workspace and in the joint space for parallel manipulators. In opposite to the serial manipulators, the parallel manipulators can admit not only multiple inverse kinematic solutions, but also multiple direct kinematic solutions. The notion of aspect introduced for serial manipulators in [Borrel 86], and redefined for parallel manipulators with only one inverse kinematic solution in [Wenger 1997], is redefined for general fully parallel manipulators. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. The study of these matrices allow to respectively define the parallel and the serial singularities. The notion of working modes is introduced to separate inverse kinematic solutions. Thus, we can find out domains of the workspace and the joint space exempt of singularity. Application of this study is the moveability analysis in the workspace of the manipulator as well as path-planing and control. This study is illustrated in this paper with a RR-RRR planar parallel manipulator.

SUMMARYIn this paper, a new family of 3-degree-of-freedom planar parallel manipulators (PPMs), namely U-shape fixed base PPMs starting with an active prismatic joint on each leg, is proposed. In order to identify the best manipulators of this family, comparative kinematic and dynamic performance studies are performed. The kinematic performances are quantified through the local performance index, namely the kinematic isotropy. From the kinematic isotropy analysis results, it is observed thatPPR-PRP-PRP,PRP-PRP-PRP andPRR-PRP-PRP configurations have better kinematic design aspects compared to other configurations of this family of U-shape fixed base parallel configurations. Further, from the workspace analysis, it is observed that thePPR-PRP-PRP configuration has a higher value of workspace to the total area required ratio compared to other configurations. This paper also presents a comparative dynamic performance analysis of these top-three U-shape fixed base configurations in terms of dynamic driving performance measures, and energy requirements for three different (fixed base size of the manipulators) aspect ratios under two different loading conditions. From the analyses results, it is perceived that thePRP-PRP-PRP configuration is requiring lower energy and dynamic driving performances than others. These analyses are done with the help of multi-body dynamic software, namely MSC ADAMS, and the results are validated through the help of real-time experiments conducted on in-house fabricated prototypes of these three PPMs. In specific, the energy consumption is measured and compared in this study. Experimental results demonstrated that thePRP-PRP-PRP manipulator displays a considerably better performance in terms of minimum energy requirement.

Parallel mechanism is composed of a platform connected to a fixed base by some linear actuators called struts. The kinematic chains of parallel mechanism are driven by these actuators to its base and has high stiffness and low weight so it can realize high speed and accurate positioning ability. The Stewart platform is one of the parallel mechanism. In serial mechanism, the direct kinematics solution is easy, but the inverse kinematics solution is very involved. The other way, in the parallel mechanism the inverse kinematics solution is easy but the direct kinematics solution is very involved. In this paper, a new method named “origami solution” to solve the direct kinematics solution of Stewart platform is proposed and some basic equations in “origami solution” are conducted. This method is based on the “Geneqc.c” which is a computer program to get roots of general equations. In the last, the method is evaluated by some examples of the Stewart platform. The direct kinematics solution is solved in 0.01mm accuracy in about 1 second calculation time by 32 bit computer.

Prescribed flexible orientation workspace and performance comparison of non-redundant 3-DOF planar parallel mechanisms

Workspace Analysis of the 4RRR Planar Parallel Manipulator with Actuation Redundancy

This study proposes a robust controller in conjunction with the dynamic modeling of an existing three degrees of freedom planar parallel manipulator which can perform effectually in the presence of parameter uncertainties and external disturbances. The planar manipulator discussed here has three legs each with a prismatic-prismatic-revolute (3-PPR) joint configuration and located on the same plane connecting the moving platform which is in the form of an equilateral triangle. Each leg consists of an active prismatic joint, a passive prismatic joint and a passive rotary joint. The dynamic model has been obtained using the Euler-Lagrangian formulation method which is based on the kinetic and potential energies of the system. The proposed controller is based on a sliding mode control scheme with a nonlinear disturbance observer incorporated which aids in eliminating disturbances present in the system which is a result of both disturbances (internal and external disturbances) and parameter uncertainties which might arise due to un-modeled dynamics. Computer based numerical simulations are performed to demonstrate the effectiveness of the proposed control and results confirming the same in the presence of disturbances.

Multi-axis machining of a complex surface is not only efficient but also reduces workpiece set-up errors. However, engineers usually rely on experience when determining set-up orientation and often cannot finish complex surfaces in one set-up. In this paper, a rational evaluation method for workpiece orientation and configuration of machine tool before tool path planning is proposed to increase the efficiency and reliability of process planning. By incorporating the visibility cone into workspace analysis, a software module is constructed in this research for optimum workpiece orientation and configuration of machine tool. First, the configurations of three-, four- and five-axis machine tools were synthesised, and the workspace was then analysed using form-shaping function. Both position vector and normal vector of each point along the u and v directions in the machining surface were employed to calculate the visibility range as the point of the visibility cone. In 3-axis machining, all normal vectors of the surface were projected on a unit sphere. All normal vectors were ensured to be within the visibility range of the ball-mill cutter as the workpiece set-up orientation changed. In 4-axis machining, the intersection between the visibility cone of each point and the workspace was obtained by changing the set-up orientation. In 5-axis machining, according to different workspaces of 5-axis machine tools, the visibility range of the machining surface was determined to yield the intersection between the visibility cone and the workspace by changing the workpiece orientation. The proposed method for evaluating manufacturability has been demonstrated to generate optimum workpiece set-up orientation and the suitable configuration of machine tools. Tool interference with workpiece surface can be avoided, which can help improve the planning of tool path.

This paper addresses the kinematic and dynamic models of a 3-PPR parallel manipulator, which are the foundation of parallel manipulator dynamic control. Then, based on the Udwadia-Kalaba equation, a three-step procedure is exploited to realize the perfect trajectory tracking of 3-PPR parallel manipulator involving the known uncertainty. In addition, when the initial conditions are incompatible and system parameters are uncertain, we adopt the adaptive robust control method to realize approximate trajectory tracking of the planar parallel manipulator. The controller consists of three parts. The first part is the perfect control of dynamic model based on the Udwadia-Kalaba equation. The second part deals with the incompatibility of initial conditions. The third part is the robust control for system uncertainty regulated by adaptive law. Finally, on the basis of theoretical analysis, the adaptive robust control algorithm is demonstrated by simulation.

This article addressed a machine learning approach for determining a solution model for the direct kinematic problems of parallel manipulators. A 5R planar parallel manipulator was utilized for that approach because it had the solution in the closed form. Initially, a dataset was created from an inverse kinematic solution of the manipulator for one of its assembly modes. Then, this dataset was fed as the input (the joint space) and the output (the platform space) for modeling the direct kinematic solution of the manipulator using one of the machine learning algorithms, which was the decision tree. To avoid overfitting during the training, hyperparameter tuning was employed to find the best parameters for the decision tree model, which was later called the best model. Hence, the best model can be validated by using the closed form solution. If the best model failed to model the direct kinematic solution in the validation, remodeling had to be performed and executed the same steps again. For remodeling, the training dataset consisted of all assembly modes of the manipulator. Consequently, the best model after remodeling was able to present the direct kinematic solutions for all possible input domains. Unfortunately, around 5% of solutions shown a higher deviation which had to be investigated in the future.

Clearance imposes some uncontrollable degrees of freedom to a manipulator. Therefore, poor dynamic performance, low accuracy, reduction in components lifetime and generation of undesirable vibrations result in the impacts of mating parts in a clearance joint. In this study, the effects of clearance on the dynamics of a planar 3-RRR parallel manipulator are investigated. Then, an optimization algorithm for simultaneously kinematic and dynamic synthesis has been carried out to reduce these effects and improve the performance and the accuracy of the manipulator. The algorithm is based on changing the lengths and the mass distribution of the links. By combining the Lagrange equations with Lankarani–Nikravesh contact force model, a series of dynamic equations are established. Then, the highly nonlinear optimization problem is tackled via a PSO method. The last but not the least, the efficiency of the algorithm and its superiority have been demonstrated by a numerical example. We claim that the linear and angular accelerations of the links and the contact forces in the joints are bounded and evolve very smoothly in the optimal design. Finally, to verify the validity of the optimization algorithm, the planar 3-RRR parallel manipulator is modeled in MSC.ADAMS software and the simulation results are compared for the original and the optimal manipulators.

Geometric isotropy indices for workspace analysis of parallel manipulators

SUMMARYThe workspace is often a critical parameter for optimum design of parallel manipulators. Workspace shape and area are two important considerations under this. In this paper, 5-R and 3-RRR planar parallel manipulators having symmetric link lengths are considered for workspace analysis. Here, symmetric means that the lengths of the first and second links of the legs are the same in all branches. Workspace analysis for such manipulators is normally done in a nondimensional way. The determination of the workspace area is one of the important parameters in the optimum design of a manipulator, and the determination of the area in terms of nondimensional parameters is extremely difficult in the case of 3-DOF and higher-DOF manipulators. In this paper, a geometric method is presented to determine different workspace shapes and areas. Based on this, all possible shapes of workspace are presented for both 5-R and 3-RRR planar parallel manipulators. For each case, a geometrical relationship between the link lengths is determined. The geometric approach gives a closed-form expression for the area calculation, which is not possible when adopting a nondimensional approach. In addition, this approach provides relationships between workspace shape and area and link lengths.

The kinematics and dynamics characteristics of Chinese medical massage manipulation, such as pressing, kneading, rolling and pushing are studied. Based on the results of this analysis, the serial mechanical arm with six rotational joints and the end actuator with 3-DOF parallel mechanism are selected, and a new type of hybrid massage robot is proposed. The kinematic equation of the robot is set up through the D-H transformation matrix in D-H coordinate system. The direct and inverse kinematic solutions of the mechanical arm are calculated. Through the introduction of the arm-shaped mark, the inverse solution becomes unique. This shows that this mechanical arm can be in good control. The virtual prototype of this mechanical arm is built by Pro/E, and it is input to ADAMS from Mechanical/Pro. The movement simulation of the virtual prototype shows that the kinematic equation of the robot is right and this kind of hybrid massage robot can simulate the massage manipulation with very well smooth movement characteristics.