OPTIMAL CONFIGURATIONS OF KINETOSTATIC SPATIAL PARALLEL ROBOTS BASED ON PROPERTIES AND POINT OF ISOTROPY.pdf

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Optimal Configurations of Kinetostatic Spatial Parallel Robots Based on Properties and

Point of Isotropy

A. Chandrashekhar1, G. Satish Babu2 1Asst. Professor, Mechanical Engineering Department, The ICFAI Foundation for Higher

Education., Hyderabad, India 2Professor, Department of Mechanical Engineering, JNTUH College of Engineering

Hyderabad, India

International Journal of Research in Mechanical Engineering Volume 3, Issue 3, May-June, 2015, pp. 33-45

ISSN Online: 2347-5188 Print: 2347-8772, DOA: 11062015 © IASTER 2015, www.iaster.com

ABSTRACT

The kinetostatic performance of parallel robots depends mainly on its internal working space configurations and its structure. A parallel robot can be said isotropic; at least a point of its working space exhibits some kind of kinetostatic properties which are homogeneous in all directions, explored using manipulability ellipsoid or isotropy. These isotropies are defined in terms of the Jacobian matrix or its inverse, when actuator/joints are different. This Jacobian normalization can overcome the drawbacks of classical methods; as this term defines that the joint/actuators are same, which can be proved meaningless. Thus manipulators in terms of isotropic configurations, proves this kinetostatic performance (which includes motion precision, achievable velocity and force) is identical in all directions. This kinetostatic performance and isotropy are derived on the based on the Eigen vectors and Eigenvalues of some Jacobian matrix.

Keywords: Kinetostatic Performance, Manipulators, Jacobian, Spatial Robots and Isotropy.

1. INTRODUCTION Robot Mechanical System is defined in terms of parallel robots which can be considered as an optimization problem for non redundant mechanism. This is generally done, in order to improve or to quantify the performance of the parallel robots. These parallel robots are defined as two kinematics chains which connect the base to end effectors and its optimal design is done based on the sensitivity to its dimensions [8]. When the sensitivity of dimensions is taken into account, it is necessary to inbuilt the concepts of Jacobian and its inverse matrices to examine the position accuracy of its end effectors. The performance indices can be calculated based on this Jacobian matrix, which is mapped as a joint rate vector into a Cartesian velocity vector. Ellipsoid associated with the mapping of these vectors based on Jacobian matrix can improve kinetostatic performance [10]. These parallel robots find its application in positioning devices, packaging, medical field etc. A dimensionless quality index based on the ratio of the Jacobian determinant with an absolute maximum value can be applied to parallel manipulators, when the inverse of the Jacobian matrix is not taken into account. To improve the kinetostatic performances of a parallel robot from different viewpoints; various metrics need to be taken into account like manipulability, workspace, service angle, number of joints and mutual deposition of the joints [16]

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The condition number for a give matrix is calculated based on the inverse of the Jacobian matrix, thus for a given square matrix, amplification is done based on a relatively round off-error method which reduces the figure of merit for maximum accuracy while designing a manipulator. Thus the dimensional inhomogeneity of the Jacobian matrix [20] entries prevents condition number as a measure of Jacobian invertibility.

Thus the condition number matrix M, with based on Frobenius norm, produces a condition number which is analytically in terms of its posture performance is defined as

This condition number analysis is done to improve the kinetostatic performance of spatial manipulators with multiple inverse matrices. As discussed computing singular values are a quite difficult task because they do not have the same values or units, which makes this condition number a meaningless one. Also, this singular value cannot be arranged in an order, so Jacobian can be normalized based on normalizing lengths. This random ordering of normalizing lengths could be avoided based on calculating characteristic lengths [serial robots]. This condition number provides a local indication for spatial parallel robots. In order to emphasize the robot interaction Global Conditioning Indices (GCI) has to be taken into account such that computational problem while calculating local indication can be avoided. This GCI provides average and extreme values of kinetostatic performance, which is an important design factor in terms of spatial parallel robots, but its main disadvantage is its robust calculation. Additionally scaling factors are considered to learn the nature of actuators which can express the kinetostatic performances in terms of specific maximum velocity and force in the adopted actuators to propose actuator’s maximum achievable performances. Physical and concrete values can be provided in terms of maximum achievable velocity (in case of velocity ellipsoid) and maximum performable force (in case of torque ellipsoid) [base paper].

2. LITERATURE REVIEW G. Nawratil, 2007 demonstrated about the new performance indices for 6R robots [1]. They demonstrated four new execution lists for control which have each of the six properties.Two of them rely on upon the end-effector and the other two don't. The EE dependent indices and are based on the operation ellipsoid and on an object-oriented metric in the workspace. It also demonstrated that can be seen as an exceptional instant of . Hence it was conceivable to give a geometric interpretation of the characteristic length. The EE independent indices and

reflects the separation of the actual posture from the nearest peculiarity. These separation measures consider the conceivable variation of the joint axes into account, because they are in view of a linearized approximation of direct kinematics.

Fig.1. Graphs of MPB(K),



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The graphs of the EE independent performance indices were displayed above. Where, and

are singular configurations. indicated the closeness to the next singularity at least as good as MPB(K), but these indices have the big advantage of being invariant under similarities and of having a geometric meaning for the 6R robot.

Pekka Pessi et.al, 2007 proposed that a mobile robot with parallel kinematics to meet the requirements for assembling and machining the ITER vacuum vessel [2]. They demonstrated that a water hydraulic cylinder and electrical motors was driven by parallel robot that has been created to get together and repair the Vacuum Vessel of ITER (International Thermonuclear Experimental Reactor). It could precisely and steadily hold all the essential machining and welding end-effectors. The kinematic models were exceptionally confounded because of the superfluous structure of the robot. They have been given independently for the Hexa-WHand the carriage mechanism. The virtual model of the robot was manufactured to exhibit distinctive control techniques for the robot. The consequences of the mechanical adaptability model demonstrated that IWR has the required stiffness.

The following form shows the stiffness matrix of the parallel manipulator has: Where,

is a diagonal matrix where the terms are spring constants of each cylinder. M. Ruggiu, 2007 surveyed on Kinematics analysis of the CUR translational manipulator [3]. He displayed a novel parallel mechanism with a CUR-based architecture of the 5-dof leg class of TPM. In the system, thus proposed the revolute (R) pair of the cylindrical joint connected to the base is viewed as being activated, along these lines giving a straightforward kinematics analysis. The kinematics analysis has been developed comprehensively, and the type of motion was demonstrated, by method for which the forward and inverse equations in position and velocity were also found. The manipulator has no rotational singularities, yet just translational singularities at a few purposes of the limits of the real workspace.

Cai-Hua Xiong et.al, 2008 demonstrated geometric parameter optimization in multi-axis machining [4]. They mainly centralized on geometric machining parameter enhancement to enhance machining accuracy issue of geometric machining parameter optimization was formed as a compelled nonlinear programming problem. The objective was to maximize the similarity between the desired surface and the actual surface under imperatives for example, non-interference conditions, geometrical design requirements of the cutter, and scallop height requirement. Here, the signed distance function was built to ascertain the point-surface distance which is utilized to portray the similarity. They also demonstrated that the pattern search algorithm is strong effectively actualized and more prone to give a worldwide least in managing exceedingly nonlinear problems.

Chun-Liang Lin et.al, 2008 proposed singularity characterization and path planning of a new 3 links 6-DOFs parallel manipulator [5]. They presented peculiarity portrayal and path planning design for another three legs six-DOFs parallel manipulator. For the manipulator, its stage has three straight slideways activated by three direct DC motors, its three extensible vertical connections interfacing the upper and base platforms were individually, incited by an inductive AC servo motor. Another methodology for looking the manipulator’s singularities based on the GA was created. Through the additional frameshift operations of enzyme and virus, his ideal way was demonstrated to have the capacity to produce a shorter and more effective way than the customary binary-GA.



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Marc Arsenault et. al, 2008 demonstrated Kinematic and static analysis of a 3-PUPS spatial tensegrity mechanism [6]. They depicted that the kinematics and statics of a spatial tensegrity mechanism were dissected. Tensegrity mechanisms advantage from the way that the majority of their segments was subjected to either pliable or concretion forces. By altering the positions of the actuators, the equilibrium configurations of the mechanism could be controlled with three degrees of freedom. Then again, it was conceivable to utilize extra tensile components in order to create fortified tensegrity prisms that do not have quick versatility. These additional parts lead to an enhanced execution of the mechanism with respect to its dynamics, its imperviousness to external loads and its stiffness.

Fig. 2. 3-PUPS Tensegrity Mechanism: (A) General View and (B) Base Architecture

The mechanism’s Ai nodes are free to translate along passive prismatic joints that are symmetrically distributed in a plane as shown in above Fig. 2. The position of node Ai along its passive prismatic joint is denoted by ni. A fixed reference frame XYZ, whose origin is used to represent the mechanism’s base, is attached to the point of intersection of the passive prismatic joints with its Y-axis directed towards node A3 and its Z-axis perpendicular on the plane formed by nodes A1A2A3. Meanwhile, a mobile reference frame X0Y 0Z0 representing the mechanism’s effector is defined as being attached to the geometric center of nodes C1C2C3 with its Y-axis directed towards node C3 and its Z-axis perpendicular to the plane formed by nodes C1C2C3. Finally, the prismatic actuators are connected to nodes Ai by passive universal joints and to the cables at nodes Ci by passive spherical joints. It can be mentioned, however, that these spherical joints may be omitted because of the cable’s flexibility. Sanjay E. Sarma et.al, 2009 surveyed on a hybrid 5-axis CNC milling machine [7]. They explored the kinematic properties of parallel and serial component mechanisms and pointed out few kinematic and structural challenges in the common sense arrangement of these machines. The hybrid concept utilized the advantages of serial and parallel mechanisms, and evades the vast majority of these pitfalls. It brought up that a 3-dof planar parallel mechanism with wide struts can't evade over-constraints and sensitivity to manufacturing tolerances. They demonstrated the impacts of these overconstraints could be stayed away by setting all the sliding joints on a single plane. However, the impacts of these tolerances relied on the measure of the structure, which suggested that the hybrid planar mechanism was more pertinent to small machine tools and does not scale well with size. The 1st mode frequency of the MIT-SS-1 was high as 104.5 Hz, which suggested that the MIT-SS-1 have the potential for high-speed machining. And finally, it exhibited that hybrid mechanisms were possible alluring candidates for small 5-axis machine tool applications.

Bakir Lacevic et.al,2010 proposed Kinetostatic Danger Field - a Novel Safety Assessment for Human-Robot Interaction [8].They presented a novel system for assessing the threat level in the vicinity of a robot manipulator. The system remained upon the presented idea of kinetostatic danger field that is the speculation of surely understood potential field approach.Two primary contrasts were that the danger field captures both the posture and the velocity of the robot and that the source of the field was the robot itself, rather than the subject/obstacle other than the exhaustive data about the peril



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level, the danger field gives off an impression of being the helpful control tool that expanded the level of security in the connection. Another advantage of the strategy depicted was the closed form possibility that takes into account the continuous applications. The strategy displayed was subjected to recreations for multi DOF robot.

The angle between the gradients, DF(r, , ) and DF(r, , 0) is such that:

Where, is the nabla operator.

G. Legnani et. al, 2010 proposed Cheope: A new reconfigurable redundant manipulator [9]. They demonstrated that all the primary parts of the kinematical qualities of the Cheope manipulator have been displayed. Direct and inverse kinematics have been created and diagnostic articulations of the direct, inverse, structural and constraint singularities was obtained. An relevance basis for the disposal of joint backlash in the repetitive activated setup have been proposed and also confirmed. These outcomes together with the examination of the workspace, have guaranteed the outline of a robot of satisfactory kinematic behavior. The decision of high performance mechanical components (mainly the linear motors) have delivered a similarly good dynamic response. Cheope, at first planned as a model for restorative applications, could be advantageously connected in different fields (machining, surface finishing, assembly tasks, etc).Her, the new parallel kinematic structure,analyzing the singularities, the workspace and the advantages of the excess setup were displayed. Aria Alasty et. al, 2010 demonstrated a Experimental kinematic calibration of parallel manipulators using a relative position error measurement system [10]. They introduced an calibration method for parallel robots where the platform was commanded few arrangements of stances and in every arrangement of postures, wanted positions were same, however, introductions were distinctive. This system utilized just only data of the input joint variables and position differences measured by a simple measurement device. The simulations demonstrated that measurement data of one point cannot adjust the robot. It also demonstrated that by expanding the number of points and number of orientations, better adjustment results could be acquired and the legitimacy of the alignment system was checked by genuine investigations directed on the Hexaglide parallel robot. The accompanying advantages could be portrayed for this strategy: relevant to more than 4 DOF parallel robots, simple establishment of gadgets for calibration and no need of internal sensors or external measurement devices to gauge the introduction of the moving platform with respect to the base platform. Zhang Jia-fan et. al, 2010 proposed a 5-Link model based gait trajectory adoption control strategies of the gait rehabilitation exoskeleton for post-stroke patients [11]. Their work managed a gait trajectory adoption control strategy based on 5-link model for the gait rehabilitation exoskeleton system. Contrasted and the current position control method, the proposed control technique could alter the gait trajectory in a manner that was fancied by the human subject as indicated by the deviation of the joint driving torques. It makes the preparation more customized and agreeable. Since the diverse human subject has distinctive physical highlighted data, a least square method based 5-link model optimization algorithm was additionally exhibited. With the model optimization it could adequately alter the model parameters naturally to fit the human subject as per the joint driving torques in position control. The consequences of the analyses with eight healthy volunteers and three stroke patients were empowering.



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The man-exoskeleton can be expressed as follows:

Where, means the joint driving torque of the exoskeleton; F is the term related to the body-

weight supported force; H , C and G specify the inertia, coriolis and gravity moment respectively, of the human subject (index man) and the exoskeleton (index exo); is the reacting joint torques from the human subject active muscle contributions. Alberto Traslosheros et. al, 2011 surveyed about a method for Kinematic Calibration of a Parallel Robot by using one camera in hand and a spherical object [12]. They explained that how to enhance precision of a parallel robot that is propelled in the Delta robot. The technique was tested by means of a visual controller and errors in the controller and the velocity of an object were utilized to acquire an index. Subsequently,both collections (nominal and corrected) of kinematic parameters were analyzed. The contrast between parameters calibrated and non calibrated have strong influence on the performance of the error in the visual controller. In this way the performance of a tracking, visual controller was enhanced despite the fact that the correction of the parameters was extremely small (errors in the controller are reduced more than 3% when the robot is calibrated). In this paper, three fundamental themes were examined: 1. Obtaining of a kinematic model based on incremental and measurements. 2. Obtaining of a 3D estimation method from one camera in hand. 3.The obtaining of the impact of small kinematical errors in a traditional visual controller. Portman et. al, 2012 demonstrated a workspace of parallel kinematics machines with minimum stiffness limits: Collinear stiffness value based approach [13]. They clarified that the collinear stiffness value (CSV) idea connected with a given setup of a parallel robot was considered. The CSV permits successful stiffness evaluation as connected to both singular and regular configurations. The CSV definition incorporates two correlative ideas: rotational and translational stiffness values (RotCSV and TrCSV, respectively). Their minimum values exhibited the eigenvalues of the 3×3 equivalent rotational stiffness matrix and the 3×3 translational stiffness block-matrices, individually. In both regular and singular configurations, the minimum CSV gave a satisfactory assessment of the stiffness properties. It could be utilized as the local stiffness performance index associated with a present arrangement and as the worldwide performance index to fix the working volume, wherein the minimal CSV fulfilled the recommended stiffness limits. Moreover, it could be considered as a safety barrier averting way to deal with singular configurations, where the minimal RotCSV takes zero value. As an application of the developed approach, the workspace of the GSP mechanism satisfying specific stiffness limits was investigated.

Zhang Yanbinn et. al, 2012 framed kinematics analysis of an asymmetrical 3-dof spatial parallel manipulator [14]. They introduced that two-translation and one-rotational degrees of freedom were displayed. The output characteristic of the moving platform was analyzed based on the screw theory.Mobility analysis and kinematic problems of the mechanism have been discussed. In terms of the velocity equation, the Jacobian of the parallel manipulator is a 33 Identity matrix, there exists no any singular configurations in the entire workspace. Additionally, the condition number of the Jacobian was constantly equivalent to one, so this manipulator was completely isotropic. This sort of mechanism performed well with regard to force and motion transmission. Fig. 3. The Novel Parallel Manipulator



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The new parallel robotic manipulator is shown in above figure, which consists of a moving platform connected with a fixed base by three limbs. The first limb was made up of two prismatic pairs and one revolute joint. The axes of the first two prismatic pairs, 1 P and 2 P, are normal to each other and the axes of joints 2 P and 3 R have been parallel. So the structure ofthe first limb could be described as P1 ⊥ P2 //R3. The second limb consists of one cylindrical pair and two revolute joints and all axes of these joints are parallel to each other, i.e., // // . The third was composed of one revolute, one prismatic and two universal joints. The arrangement sequence of these joints from the base to the platform is − − − , where P, R, C and U denote the prismatic, revolute, cylindrical and universal joints, respectively. Morteza Daneshmand et.al, 2013 survived on a topic kinematic sensitivity and workspace optimization of planar parallel mechanisms using evolutionary techniques [15]. They explored the kinetostatic performance of the planar parallel mechanisms. Their geometrical measurements were liable to be enhanced taking into account their execution criteria, including point-displacement and rotational kinematic sensitivity and also workspace. Likewise, it was inferred that the 3-PRR has a satisfactory kinematic sensitivity concerning the other planar parallel mechanisms. The consequences of the multiobjective optimization uncovered that the Pareto points for the 3-RRR and 3-RRR overwhelmed the ones for the other planar parallel mechanisms with revolute actuators and the Pareto points for the 3-RPE dominated the ones for the 3-REP, which was promptly an indication of the better execution of the previous, regarding the greater part of the three destinations.

Matteo Verotti et.al, 2013 demonstrated a Kinetostatic Optimization of a MEMS–Based Compliant 3 DOF Plane Parallel Platform [16]. They gave an algorithm for the forward kinetostatic analysis of plane parallel manipulators have been exhibited. The technique, which have been portrayed in subtle element, ended up being quick and strong, and accordingly it has been utilized as a device for optimization purposes. A genetic algorithms have been connected to five diverse target capacities which made utilization of the new strategy. As indicated by the outcomes, the proposed optimization process should be intriguing for designing the manipulator geometry so as to accomplish a great performance index. At long last, a kinematic condition guide has been displayed with a specific end goal to demonstrate the sensibility of the proposed lists from the varieties of some link lengths.

Fig. 4 Graph A) and Kinematic Chain B) of the Florida Shoulder Plane Platform

In the present investigation a method for the forward kinematic analysis of a parallel plane robot, called Florida Shoulder, has been proposed. This procedure has been applied to evaluate two indices, namely, kinematic condition number k(J) and the mechanical advantage MA. The first index gives a good esteem of the sensitivity of the tip velocities upon directions, while the second could be used to evaluate the overall force amplification factor in static conditions. The two indices have been used as fitness function by an optimization process that was based on a Genetic Algorithm, and so some optimal structures have been identified.



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F. Courreges et. al, 2013 demonstrated a New human-centered kinetostatic criteria for tele-operated robots,validation with medical tele-sonography robots [17]. They proposed that FCGKPI was convincingly more qualified than established files for physically teleoperated robots to anticipate the end-client fulfillment and ought to be considered as a basis for robot configuration and assessment.Its maximum capacity was achieved this foundation ought to be summed up for parallel and kinematically repetitive robots and for inhomogenous robots.For any serial robotic manipulator having numerous arrangements outside singularities, executing a task T, and for any local kinematic criterion (q) increasing with the performance ; the GKPI denoted “Free Contortion GKPI with respect to ” (FCGKP ) is defined as:

Qinchuan Li et. al, 2013 demonstrated the Geometrical distribution of rotational axes of 3- [P] [S] parallel mechanisms [18].They deliberately examined the rotational axes of 3- [P] [S] PMs with distinctive limb arrangements. In view of the geometrically condition of LPs and spherical joint centers, the 3-PRS PMs characterized into four classifications and seven subcategories.Reciprocal screw theory connected to recognize of the rotational axes of the 3-PRS PM. It was demonstrated that the presence of a limited rotational axis depends on the geometrical condition of LPs and spherical joint centers. The outcomes likewise help to elucidate the revolution capacities of the 3- [P] [S] PM. Maciej Petko et. al, 2013 demonstrated about the Acceleration of Parallel Robot Kinematic Calculations in FPGA [19]. They showed that how to increase the effectiveness of parallel robot kinematic estimations by custom processor instructions. The processing, parallel robot was given its kinematic structure and solution of the inverse kinematics problem. The accelerator featured in the paper expanded the standard floating-point capabilities of the Nios II processor ALU with additional floating-point instructions. The calculation speed expanded more than four times and very nearly five times, though the number of utilizing logical elements expanded by 11% and 65% for instructions C1 and C2 respectively. The manifestation of kinematic equations allows for parallelizing of some operations that also could shorten the time of calculations. Kinematics equations of parallel robots differ essentially with regard to complexity and the sort of contained arithmetic operations and functions. In this way, for every kinematic structure of a parallel robot a specialized accelerator was required. His methodology introduced in the paper could be connected to develop an accelerator for any parallel robot.

The custom instruction must be called twice to complete calculations :

; ; where: C1, C2 – hardware instructions, f – arithmetic function, a, b, c, m, x – data, 32-bits float.

Amir Rezaei et. al, 2013 explained a Position, Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator [20]. They obtained an analytical solution for the Invkinin XYZ mode, a numerical answer for the Invkinin in Z mode and analytical solution for Dirkin with special arrangement was obtained, the velocity and acceleration inversion, obtaining the direct and inverse Jacobians were displayed, Jacobian of constraints as well as introducing non- pure rotational and non-



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pure translational Jacobian matrices, the conventional types of singularities as well as constraint singularity using the Jacobian of constraints matrix were investigated, two methods for obtaining robot workspaces in two operational modes was presented and finally examined the impact of tool length on the XYZ workspace. Mohsen Asgari et. al, 2013 survived about Dynamics and Control of a Novel 3-DoF Spatial Parallel Robot [21]. They exhibited that the a new structure of spatial parallel manipulator with three degrees of pure translational freedom from DELTA robot family was exhibited. At first, the inverse kinematic model of the robot has been completed. For inverse kinematic problem, these solutions exhibit that, in general, there were conceivable stances for each limb. After that the Jacobian matrix was inferred analytically. At that point, by utilizing the standard of virtual work,the inverse dynamic model has been established.This technique was superior to the basic C-T method with a conventional controller in trajectory tracking and particularly adjusting itself to aggravation conditions.It ought to be noticed that the robotic system with disturbance problems apparently contains common problems, as a special class. In this way, the proposed control strategy is broadly pertinent to control of any robotic systems. Javier Ruiz-Garc´ıa et. al, 2013 proposed about Direct Kinematics of a 6-PUS Parallel Robot Using a Numeric-Geometric Method [22]. They clarified that a very general methodology to obtain the direct kinematics of any parallel robot utilizing an iterative algorithm and this algorithm was executed for the robot examined in this paper.This proposed method additionally took less time to compute. In spite of the fact that it took less time, 7 seconds is still a huge measure of time so as to execute this on real time. Some options to reduce the computation time was: using a faster processor, using parallel processing to calculate the distances between the points of the arcs, or discriminating more angles of the arcs, 15◦ instead 10◦.It is essential to note that the technique works because the configuration 6-3 simplifies each pair of legs, as one leg with only one degree of freedom. This is an exceptionally valuable method when working with parallel manipulators. Bingtuan Gao et. al, 2013 demonstrated inverse kinematics and workspace analysis of a bio-inspired flexible parallel robot [23]. They showed that a bio-inspired adaptable parallel robot whose moving platform and the base were joined with adaptive supportive compression springs spine and 3 driving cables. Inverse kinematics and WCW of the robot were examined and numerical actualized. It was demonstrated that the inverse position of the robot illuminated by consolidated the power and torque balance equations together with the lateral bending equations of the springs spine. Numerical implementations demonstrated that the translational WCW was an inverted cone and generally the volume of the translational WCW of the robot will increase as the increase of value a/b (connecting radii of the driving cables w. r. t. the base to the moving platform). Crane et. al, 2013 demonstrated Reverse kinetostatic analysis and stiffness synthesis of a spatial tensegrity-based compliant mechanism [24]. His paper concentrates on two problems for a spatial tensegrity-based compliant mechanism. The conclusions are per the following:

In the first problem, the reverse kinetostatic issue, the lengths of the seven leg pistons and the force magnitudes in the seven springs were scientifically discovered that would position and arrange the top body as craved so it is in equilibrium when a known external wrench was connected. It was demonstrated that two real solutions could exist. As two sub problems of the first problem, the solutions for the minimum potential energy in the seven springs and for following the given desired path of the origin and orientation of the top body coordinate system were exhibited.



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In the second problem, the stiffness synthesis problem, the seven spring constants and seven piston lengths were determined to position and situated the top body as determined while in equilibrium under a given connected external wrench. Likewise the sought stiffness matrix for the mechanism was indicated. A unique solution is obtained unless certain geometric conditions happen, which cause a 14 × 14 matrix to become singular or be near to partic.

Matteo Parigi Polverini et. al, 2014 Real-Time Collision Avoidance in Human-Robot Interaction Based on Kinetostatic Safety Field [25]. They remained upon the presented idea of kinetostatic safety field, have been given. The safety field was a novel safety evaluation for assessing the peril level in the region of an inflexible body proposed as a source of danger and represented the expansion of the aggregated risk field idea to moving surfaces or bodies. Two primary commitments were that the safety field captured both relative position and relative velocity between the source of danger and the point where the field was figured. Likewise, it relied on upon the shape and size of the source of danger as opposed to interestingly on its length. Besides, the presentation of a reference frame local to the rigid body and the subsequent shut structure processability took into consideration continuous reckoning of the safety field for entangled shapes and for a whole manipulator. In a brief moment, step a safety field based control for multi-DOF redundant manipulators have been proposed, that permitted both self-collision avoidance and human-robot coexistence to be accomplished. Test results on the ABB FRIDA dual arm robot upheld this approach. The Cumulative Kinetostatic Safety Field (CKSSF) is defined as the following surface integral:

Where, A denotes the area of the triangular surface. Reza Emami et. al, 2014 demonstrated a generalized exponential formula for forward and differential kinematics of open-chain multi-body systems [26]. They clarified that an expansion of the result of generic open-chain multi-body systems with multi-d.o.f., holonomic and nonholonomic joints was formalized utilizing Lie group theory and differential geometry. Towards this objective, multi-DoF joints were arranged and the thought of displacement subgroup was summed up. It was demonstrated that the relative configuration manifolds of such joints were Lie groups, and the exponential map was suggestive for a wide range of displacement subgroups aside from one type. The screw joint parameters were characterized, and their association with the excellent joint parameters was formalized.The nonholonomic constraints in the Pfaffian form were considered on displacement subgroups, and presented an allowable screw joint speeds the Jacobian of an open-chain multi-body system was adjusted, accordingly. The proposed summed up the exponential definition for Forward and Differential Kinematics was autonomous of the intermediate coordinate task to the bodies and the decision of the joint parameterization and a premise for the Lie algebra of the relative configuration manifold. The computational parts of the created definition were investigated through an illustration where Forward and differential Kinematics of a mobile manipulator mounted on a spacecraft were calculated. Catalin Alexandru et. al, 2014 surveyed on a paper modeling the angular capability of the ball joints in a complex mechanism with two degrees of mobility [27]. They concentrated on the complexity of the guiding mechanism in the study required the thought of the reference outlines for every one of its components/ bodies, in which the particular geometric parameters of the component were characterized. The structural complexity of the mechanical system was determined not only by the multitude of geometric parameters, as well as by the degrees of portability of the mechanism (being a bi-mobile mechanism), with total and partial mobility. The kinematic unpredictability of the mechanical system was dictated by its structural-geometric complexity and also by the multitude of kinematic functions that characterized the usefulness of guiding (suspension and steering) mechanism.



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As per its functionality (with two degrees of mobility), the maximum travels of the suspension, coupled with the maximum steering rotations, delimited the extreme socket size were in the study of guiding system. The numeric simulations have permitted to acquire theoretical and practical information of real value. Meng-Shiun Tsai et. al, 2014 demonstrated A novel approach for forward dynamic analysis of a 3-PRS parallel manipulator with consideration of the friction effect [28]. They demonstrated a novel decomposition methodology was proposed for forward dynamic analysis of a 3-PRS parallel manipulator. In the view of decomposition of their action forces, a Jacobian matrix which could amplify the dynamic forces of the moving platform from the tasks pace into the joint space was resolved. A sufficient condition was given in a lemma to guarantee the presence of the Jacobian matrix. The proposed system could prompt decay the estimation of an inverse of 21×21 augmented matrix into that of 6×6 and 15×15 matrices in solving forward dynamic problem. The computational effectiveness could subsequently be enhanced as com- pared with the conventional methodology. Moreover the displayed forward dynamic model could give a basic premise to further investigation about the compensation of the friction forces.

Fig. 5. Block Diagram of the Forward Dynamic Model Considering Friction Forces

Zhang Fei et. al, 2014 demonstrated mobility analysis and kinematics simulation of the spatial parallel automatic gear shifter [29]. They clarified that based on the configuration of the mechanical structure of the Spatial Parallel Automatic Gear Shifter, the important qualities of the automatic gear shifter was presented and mobility of the mechanical structure was additionally investigated. The mobility analysis results demonstrated that automatic gear shifter has 2-spatial-DOF. With the space force closure principle of the parallel robots, we got the association between rotating angle inputs and the spatial location of the shift lever which provided method to drive the gear shifter. The 2093 simulation in ADAMS worked well with the method and got kinematic analysis results and the kinematic analysis also demonstrated that the automatic gear shifter can not only decouple the movement of the X and Y direction but also has motion in the Z direction. It implied that the automatic gear shifter could control the shift lever move smoothly and precisely without damaging the vehicle structure. Through this exploration results,he affirms the Spatial Parallel Automatic Gear Shifter met the greater part of the prerequisites of type gear shift. Yi Lu et. al, 2014 demonstrated Kinetostatic analysis of a novel 6-DoF 3UPS parallel manipulator with multi-fingers [30]. They derived the logical formulae for understanding the kinetostatics of the proposed PM with multi-fingers. The kinetostatics expository solutions of the proposed PM with multi-fingers were checked by simulation solutions of simulation mechanisms generated in Matlab/Simulink/Mechanics. The proposed PM with multi-fingers have the accompanying merits: Three fingers could be introduced onto the moving platform without obstruction; and multi-fingers



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has an extensive workspace. It has potential applications in forging operator, assembly cells of flexible manufacturing system, parallel machine tools, dexterous hand of a surgical manipulator, micro-manipulators, tunnel borer, rescue robots, and satellite surveillance platform manufacturing, CT-guided surgery, and micro-nano operation of bio-medicine. 3. SUMMARY A kinetostatic model based on isotropic behaviour from a non isotropic behaviour is essential for spatial parallel robots, since it can exhibit similar behaviour in all axis. This kinetostatic behaviour is improved based on jacobian matrix and condition numbering; this architect can provide a better performance than kinematic behaviour because it can be used only to find the range of movement for a given mechanism.Using this kinetostatic behaviour multiple DoF constraints could be handled as it exhibits isotropic behaviour in all its directions. REFERENCES [1] G. Nawratil (2007). Enumeration of a Class of Over Constrained Mechanisms Using the

Theory Od Reciprocal Screws. Mechanism and Machine Theory. pp. 1499–1511.

[2] Pekka Pessi et.al (2007). A Mobile Robot with Parallel Kinematics to Meet the Requirements for Assembling and Machining the ITER Vacuum Vessel. Fusion Engineering and Design. pp. 2047-2054

[3] M.Ruggiu (2007). Kinematics Analysis of the CUR Translational Manipulator. Mechanism and Machine Theory. pp. 1087–1098.

[4] Cai-Hua Xiong et.al (2008). Geometric Parameter Optimization in Multi-Axis Machining. Computer-Aided Design. pp. 879–890.

[5] Chun-Liang Lin et.al(2008). Singularity Characterization and Path Planning of a New3 Links 6-DOFs Parallel Manipulator.European journal of control.. DOI:10.3166/EJC.14.201–212. pp.201-212.

[6] Marc Arsenault et.al(2008). Kinematic and Static Analysis of a 3-PUPS Spatial Tensegrity Mechanism. Mechanism and Machine Theory. pp. 162-179.

[7] Sanjay E. Sarma et.al (2009). A Hybrid 5-Axis CNC Milling Machine. Precision Engineering. pp. 430-446.

[8] Bakir Lacevic et.al (2010). Kinetostatic Danger Field - a Novel Safety Assessment for Human-Robot Interaction. IEEE/RSJ International Conference on Intelligent Robots and Systems. pp. 2169-2174.

[9] G. Legnani et.al (2010). Cheope: A New Reconfigurable Redundant Manipulator. Mechanism and Machine Theory. pp. 611–626.

[10] Aria Alasty et.al (2010). Experimental Kinematic Calibration of Parallel Manipulators Using a Relative Position Error Measurement System. Robotics and Computer-Integrated Manufacturing. pp. 799-801.

[11] Zhang Jia-fan et.al (2010). 5-Link Model Based Gait Trajectory Adaption Control Strategies of the Gait Rehabilitation Exoskeleton for Post-Stroke Patients. Mechatronics. pp. 368-376.

[12] Alberto Traslosheros et.al (2011). A Method for Kinematic Calibration of a Parallel Robot by Using One Camera in Hand and a Spherical Object. The 15th International Conference on Advanced Robotics. pp. 75-81.

[13] V.T. Portman et.al (2012). Workspace of Parallel Kinematics Machines with Minimum Stiffness Limits: Collinear Stiffness Value Based Approach. Mechanism and Machine Theory. pp. 67-86.



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[14] Zhang Yanbinn et.al (2012). Kinematics Analysis of an Asymmetrical 3-DOF Spatial Parallel Manipulator. Third International Conference on Digital Manufacturing & Automation. pp. 507-509.

[15] Morteza Daneshmand et.al (2013). Kinematic Sensitivity and Workspace Optimization of Planar Parallel Mechanisms Using Evolutionary Techniques. RSU/ISM International Conference on Robotics and Mechatronics. pp. 384-389.

[16] Matteo Verotti et.al (2013). Kinetostatic Optimization of a MEMS–Based Compliant 3 DOF Plane Parallel Platform. IEEE 9th International Conference on Computational Cybernetics. pp. 261-266.

[17] F. Courreges et.al (2013). New Human-Centered Kinetostatic Criteria for Tele-Operated Robots, Validation with Medical Tele-Sonography Robots. IEEE conferences. pp. 1-5

[18] Qinchuan Li et.al (2013). Geometrical Distribution of Rotational Axes of 3- [P] [S] Parallel Mechanisms. Mechanism and Machine Theory. pp. 46-57.

[19] Maciej Petko et.al (2013) . Acceleration of Parallel Robot Kinematic Calculations in FPGA. IEEE conferences on Robotics and Mechatronics. pp. 34-39.

[20] Amir Rezaei et.al (2013). Position, Jacobian and Workspace Analysis of a 3-PSP Spatial Parallel Manipulator. Robotics and Computer-Integrated Manufacturing. pp. 158-173.

[21] Mohsen Asgari et.al (2013). Dynamics and Control of a Novel 3-DoF Spatial Parallel Robot. Mechanism and Machine Theory pp. 611-626.

[22] Javier Ruiz-Garcia et.al (2013). Direct Kinematics of a 6-PUS Parallel Robot Using a Numeric-Geometric Method. IEEE International Conference on Mechatronics, Electronics and Automotive Engineering. pp. 46-50.

[23] Bingtuan Gao et.al (2013) . Inverse Kinematics and Workspace Analysis of a Bio-inspired Flexible Parallel Robot. IEEE International Conference on Cyber Technology in Automation, Control and Intelligent Systems. pp. 138-143.

[24] C.D. Crane III et.al (2013). Reverse Kinetostatic Analysis and Stiffness Synthesis of a Spatial Tensegrity-Based Compliant Mechanism. Mechanism and Machine Theory. pp. 320-337.

[25] Matteo Parigi Polverini et.al (2014). Real-Time Collision Avoidance in Human-Robot Interaction Based on Kinetostatic Safety Field. IEEE/RSJ International Conference on Intelligent Robots and Systems. pp. 4136-4141.

[26] M. Reza Emami et.al (2014). A Generalized Exponential Formula for Forward and Differential Kinematics of Open-Chain Multi-Body Systems. Mechanism and Machine Theory. pp. 61-75.

[27] Catalin Alexandru et.al (2014). Modeling the Angular Capability of the Ball Joints in a Complex Mechanism with Two Degrees of Mobility. Applied Mathematical Modelling. pp. 5456–5470.

[28] Meng-Shiun Tsai et.al (2014). A Novel Approach for Forward Dynamic Analysis of 3-PRS Parallel Manipulator with Consideration of Friction Effect. Robotics and Computer-Integrated Manufacturing. pp. 315–325.

[29] ZHANG Fei et.al (2014). Mobility Analysis and Kinematics Simulation of the Spatial Parallel Automatic Gear Shifter. IEEE International Conf. on Mechatronics and Automation. pp.2089-2094.

[30] Yi Lu et.al (2014). Kinetostatic Analysis of A Novel 6-Dof 3UPS Parallel Manipulator with Multi-Fingers. Mechanism and Machine Theory. pp. 36-50.


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OPTIMAL CONFIGURATIONS OF KINETOSTATIC SPATIAL PARALLEL ROBOTS BASED ON PROPERTIES AND POINT OF ISOTROPY.pdf