Fig 7 - uploaded by Leonardo Jelenković
Content may be subject to copyright.
Hexapod with fixed strut lengths Inverse kinematics for this model is slightly more complex from standard hexapod and can be computed using equations:
Source publication
The aim of this work is to combine different mathematical representations of the forward kinematics problem with various optimization algorithms and find a suitable combination that may be utilized in real -time environment. Additionally, we note the existence of equivalent trajectories of the mobile platform and suggest an adaptation to the solvin...
Similar publications
Lattice calculation of $B\to D^{(*)}\ell\bar\nu$ decay form factors is now available from multiple lattice collaborations for both zero-recoil limit and non-zero recoil kinematics. Yet, there are a number of challenges we face to better control the systematic errors and to extend the application of lattice calculations to related quantities. The su...
Citations
... In their 2011 study, Xi and Fengfeng designed and analyzed a parallel mechanism with the capability to alter its configuration, as reported in their publication "Design and analysis of a parallel mechanism with the ability to change configuration" [6]. Jakobovic and Domagoj, in their 2002 publication "Unsolved problems in direct and inverse kinematics of parallel mechanisms, with a special emphasis on the Stewart mechanism" [7], examined the unresolved issues in the direct and inverse kinematics of parallel mechanisms, particularly the Stewart mechanism. Other researchers have focused their attention on the Hexaglide mechanism. ...
The objective of this research is to develop an advanced controller for CNC machines equipped with Hexaglide parallel mechanisms. While traditional CNC machines employ mechanisms with perpendicular axes, accuracy may be compromised when processing high force loads. Parallel mechanisms, such as Hexaglide, have gained attention in the CNC industry due to their ability to maintain precision at high speeds and power. However, the absence of a sophisticated controller for converting G-Code to motion paths has been a significant drawback for CNC machines with parallel mechanisms. This research proposes a solution by introducing a controller that can translate G-Code generated by code software into appropriate motion commands for the Hexaglide mechanism.
... In inverse kinematics, the actuator lengths are calculated based on the platform pose [6]. In forward kinematics, the platform pose is calculated for a given set of the actuator lengths and joint angles [7]. The mathematics and solution of inverse kinematics is much easier than forward kinematics for a hexapod. ...
... Husty [10] derived a 40th-degree univariate equation for a general 6-6 Stewart platform, by finding the greatest common divisor of the intermediate polynomials. Domagoj and Jelenkovicti [7] used canonical formulation for the forward kinematics and derived 9 equations with 9 unknowns and then solved it by multiple optimization methods. Wang and Yunfeng [11] derived the direct kinematics solutions for calculating the platform pose by increasing the actuator lengths in small amount and then increasing the joint parameters also in small amount utilizing numerical methods. ...
This paper presents a method to generate feasible, unique forward-kinematic solutions for a general Stewart platform. This is done by using inverse kinematics to obtain valid workspace data and corresponding actuator lengths for the moving
platform. For parallel kinematic machines, such as the Stewart platform, inverse kinematics are straight forward, but the forward kinematics are complex and generates multiple solutions due to the closed loop structure of the kinematic links. In this research, a simple iterative algorithm has been used employing modified Denavit-Hartenberg convention. The outcome is encouraging as this method generates a single feasible forward kinematic solution for each valid pose with the solved DH parameters and unlike earlier forward kinematics solutions, this unique solution does not need to be manually verified. Therefore, the forward kinematic solutions can be used directly for further calculations without the need for manual pose verification. This capability is essential for the six degree of freedom materials testing system developed by the authors in their laboratory. The developed system is aimed at characterizing additively manufactured materials under complex combined multiple loading conditions. The material characterization is done by enabling high precision force control on the moving platform via in situ calibration of the as-built kinematics of the Stewart Gough platform.
... The variable varies from 1 to 6, for having 6 actuators acting in the system, with 6 starts and ends equally spaced [58,59,60]. ...
... Applying the above relations allows for calculating the new length of the actuators, which is needed for control of the system position [58,60]. ...
In knee arthroplasty, a common surgery carried out on around 80,000 patients annually, long-term
pain is the most frequently noted complication. The most important factor in avoiding pain after
knee surgery and achieving the optimal outcome, is the perfect positioning of the knee during the
surgery. Existing methods of positioning the knee are not sufficient to achieve this in all patient
cases. Parallel Kinematic Machines (PKMs) are a type of robotics that lend themselves well to use
in modern surgical settings due to their flexibility, in combination with their stability and accuracy.
Previous studies have suggested that the use of these machines could allow for the most ideal and
stable positioning of the leg during surgery, thus providing the best possible outcome for the
patient. This study explores the design of a suitable PKM for use in knee arthroplasty surgery, in
order to allow surgeons to carry out knee replacements with maximum precision and provide the
most favourable patient outcome. This report outlines all stages of design for a surgical assistance
PKM robot from early research and concept generation through to prototyping. The report also
concludes on the success of this PKM prototype and outlines the suggestions for future work to be
carried out in order to progress the design to a stage ready for use in industry.
... Currently, our framework supports the estimation of lumped parameters for each DoF including the polar coordinates based on a pattern search algorithm similar to [64]. For the motion control of testing, the current framework adopts a cascaded force-position control approach, where the kinematics of the Stewart platform is estimated using the actuator positions and forward kinematics through a Newton-Raphson approximation [65]. The load conditions are measured by the printed wearable soft sensor QTSS™ (Quantum Technology Super Sensor), shown in Figure 6c. ...
Lower limb prostheses offer a solution to restore the ambulation and self-esteem of amputees. One key component is the prosthetic socket that serves as the interface between prosthetic device and amputee stump and thereby has a wide range of impacts on efficient fitting, appropriate load transmission, operational stability, and control. For the design and optimization of a prosthetic socket, an understanding of the actual intra-socket operational conditions becomes therefore necessary. This is however a difficult task due to the inherent complexity and restricted observability of socket operation. In this study, an innovative mechatronics-twin framework that integrates advanced biomechanical models and simulations with physical prototyping and dynamic operation testing for effective exploration of operational behaviors of prosthetic sockets with amputees is proposed. Within this framework, a specific Stewart manipulator is developed to enable dynamic operation testing, in particular for a well-managed generation of dynamic intra-socket loads and behaviors that are otherwise difficult to observe or realize with the real amputees. A combination of deep learning and Bayesian Inference algorithms is then employed for analyzing the intra-socket load conditions and revealing possible anomalous.
... While the forward equations for the Gough-Stewart manipulator used to determine the position, orientation, and its rate change with time in time based on the lengths of the linkages for the manipulator. The solution of the inverse kinematics equation are very easy compare with the solution of the forward kinematics equations [6]. This paper deals with the solution of the kinematics problem analysis for Gough Stewart manipulator, where solved the invers kinematics by using the position and orientation at initial and final position for the moving platform to obtained the lengths of the linkages, then used these lengths to solve the forward kinematics analysis by Newton Raphson method to obtained these position and orientation. ...
The Gough Stewart Robotic manipulator is a parallel manipulator with six-degree of freedom, which has six equations of Kinematics (Inverse and forward), with six variables (Lengths, Position, and Orientation). In this work derived the inverse equations, which used to compute the lengths of the linkages and its changes depended on the position and orientation of the platform's center, then derived the forward equations to calculate the position and orientation of the moving platform in terms of the lengths. This theoretical model of the kinematics analysis of the Gough Stewart has been built into the Simulink package in Matlab to obtain the lengths, position, and orientation for the manipulator at any time of motion. The input parameters (Position and Orientation) in inverse blocks compared with the output parameters (Position and Orientation) in the forward blocks, which show good results.
... D. Jakobovic and L. Jelenkovic [31] solved forward kinematics problem with various optimization algorithms and find a suitable combination that may be utilized in real-time environment. ...
This thesis deals with path planning of Gough-Stewart robot
manipulator with avoidance singularity configuration when a parallel robot
can pass through this configuration.
... The inverse kinematics problem of a Stewart platform [14] consists in computing the leg lengths l i given the position p and the orientation (ϕ p , θ p , ψ p ) of the mobile platform. So, the IK can be computed as described in eq. ...
The Stewart parallel mechanism is used in various applications due to its high load-carrying capacity, accuracy and stiffness, such as flight simulation, spaceship aligning, radar and satellite antenna orientation, rehabilitation applications, parallel machine tools. The dissemination of such parallel robots is however limited by three factors: the limited workspace, the singularity configurations existing inside the workspace, and the high cost. In this work, a simulation environment to support the design of a cost-effective Stewart Platform-based mechanisms for specific applications and to facilitate the choice of suitable components, e.g., linear actuators, plate sizes, is presented. The optimal design here presented has multiple objectives. It intends to maximize the payload and minimize the forces at each leg needed to counteract external forces applied to the mobile platform during positioning or manufacturing applications. These objectives can be achieved through a dynamic optimization. It also aims at avoiding reduction of the robot workspace through a kinematic optimization.
... As for inverse kinematics, it solves the problem of determination of actuators length for a given position and orientation of the mobile platform. There are several papers [13, 14] discussing on solving forward kinematics of the parallel robots. They are formulated in different ways and each has its own advantages and disadvantages. ...
This paper describes the development of motion platform for vehicle driving simulator in Universiti Teknologi Malaysia (UTM). In this project, the visual database system that simulates the driving environment and the vehicle dynamic model that computes the vehicle response are integrated with a motion platform to simulate the motion of a vehicle in virtual environment. The motion platform design is based on 6-DOF Stewart platform design configuration. An Inverse kinematics model for the Stewart Platform and Independent Vehicle Dynamic Model (iVDM) are developed using MATLAB Simulink. The independent Vehicle Dynamic Model (iVDM) serves as an agent for performance investigation of the inverse kinematics model.
... Amusement park simulators still use essentially the same system to actuate many rides. This phenomenon is discussed in a 2002 paper [26] by Jakobovic and Jakobovic, who combine several analytical models with optimization schemes to solve the forward kinematics. Their goal was to find a method that would approximate the position and location of the platform, as it was in motion, while maintaining minimal errors. ...
Motion platforms and motion cueing algorithms (MCA) have been included in virtual reality applications for several decades. They are necessary to provide suitable inertial cues in vehicle simulators. However, the great number of operational constraints that these devices and algorithms suffer, namely limited physical space, elevated costs, absence of sufficient power, difficulty of tuning and lack of standardized assessment methods, have hindered their widespread use. This work tries to clarify open questions in the field, such as: How important is MCA tuning? How much does size, number of DOF and power/latency matter? Can the absence of motion be better than poor motion cueing? What are the key factors that should be addressed to enhance the design of these devices? Although absolute certain answers cannot be given, this paper tries to clarify these research questions by performing massive experiments with simulated motion platforms of different types, sizes and powers. The information obtained from these experiments will be important to customize the design of real devices for this particular use. Ideally, subjective experiments with human experts would have been preferred. However, the use of simulated devices allows comparing many different motion platforms. In this paper, forty of these devices are simulated, optimized by means of a heuristic algorithm and compared with objective indicators in order to measure their relative performance using the classical MCA, something that would require an unreasonable amount of effort with real users and real devices. The obtained results show that MCA tuning is of the utmost importance in motion cueing. They also suggest that high power can usually compensate for lack of size and that a 6-DOF motion platform slightly improves the performance of a 3-DOF motion platform.
