• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.83.2-83
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• 2001

This paper presents a new formulation approach to reduce computational burden of the direct kinematics of 6-dof haptic devices with three sets of a parallel-serial linkage. Their direct kinematics has been formulated through employing the Denavit-Hartenberg notation, which results in complicated formulation procedures and heavy computational burden. For reducing these problems, this paper reconfigures the haptic devices into an equivalent kinematic model of the 3-6 Stewart-Gough Platform that has three connecting joints on the moving platform. Moreover, the direct kinematics of the 3-6 Platform can be effectively formulated by using the proposed Tetrahedron Approach.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.1
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• pp.144-153
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• 1997

The determination of the direct kinematics of the parallel mechanism is a difficult problem but has to be solved for any practical use. This paper presents the efficient formulation of the direct kinematics for double parallel robot arm. The robot arm consists of two parallel mechanism, which generate positional and orientational motions, respectively. These motions are decoupled by a passive central axis which is composed of four revolute joints and one prismatic joint. For a set of given lengths of linear actuators, the direct kinematics will find the joint displacements of th central axis from geometric constraints in each parallel mechanism. Then the joint displacements will be converted into the position and the orientation of the end effector of the robot arm. The proposed formulation is decoupled and compacted so that it will be implemented as a real-time direct kinematics. With the proposed formulation, we analyze the motion of the double parallel robot and show its characteristics. Specially, we investigate the workspace in terms of positional space as well as orientational space.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.2
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• pp.156-163
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• 2002

This paper presents a new formulation to simplify the three resulting constraint equations of the direct kinematics of the 3-6 (Stewart-Gough) Platform. The conventional direct kinematics of the 3-6 Platform has been formulated through complicated steps with trigonometric functions in three angle variables and thus results in the computational burden. In order to reduce the formulation complexity, we replace an angle variable into a length one and express three connecting joints on the moving platform in the same frame. The proposed formulation yields considerable abbreviation of the number of the calculation terms involved in the direct kinematics. It is verified through a series of simulation results.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.3
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• pp.97-104
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• 2003

This paper proposes a new parallel manipulator fur plane motion, and then discusses on the workspace and kinematical characteristics of the manipulator. The conventional planar parallel manipulators have some disadvantages which are complex non-closed type direct kinematics, workspaces containing useless voids, and concave type border tines of workspaces. The proposed planar parallel manipulator overcomes the above disadvantages, that is, the manipulator has simple closed type direct kinematics, a void-free workspace, and a convex type borderline of a workspace. This paper shows the simulation result of the workspace as well as performances indices using a homogeneous inverse Jacobian.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.3
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• pp.217-223
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• 2002

The paper presents a single constraint equation of the direct kinematic solution of 6-dof (Stewart-Gough) platforms. Many research works have presented a single polynomial of the direct kinematics for several 6-dof platforms. However, the formulation of the polynomial has potential problems such as complicated formulation procedures and discrimination of the actual solution from all roots. This results in heavy computational burden and time-consuming task. Thus, to overcome these problems, we use a new formulation approach, called the Tetrahedron Approach, to easily derive a single constraint equation, not a polynomial one, of the direct kinematics and use two well-known numerical iterative methods to find the solution of the single constraint equation. Their performance and characteristics are investigated through a series of simulation.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.528-537
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• 2003

This paper proposes a 3-PPR planar parallel manipulator, which consists of three active prismatic Joints, three passive prismatic joints, and three passive rotational joints. The analysis of the kinematics and the optimal design of the manipulator are also discussed. The proposed manipulator has the advantages of the closed type of direct kinematics and a void-free workspace with a convex type of borderline. For the kinematic analysis of the proposed manipulator, the direct kinematics, the inverse kinematics, and the inverse Jacobian of the manipulator are derived. After the rotational limits and the workspaces of the manipulator are investigated, the workspace of the manipulator is simulated. In addition, for the optimal design of the manipulator, the performance indices of the manipulator are investigated, and then an optimal design procedure Is carried out using Min-Max theory. Finally. one example using the optimal design is presented.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.83.4-83
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• 2001

The paper presents a new closed-form, not a polynomial-form, solution of the direct kinematics of the 3-6 (Stewart-Gough) Platform. Many research works have presented a single high-order polynomial equation of the direct kinematics. However the polynomial equation causes potential problems such as complicated formulation procedures and discrimination of the actual solution from all roots, which results in time-consuming task and heavy computational burden. Thus, to overcome these problems, we use a new formulation approach, based on the Tetrahedron Approach, to derive easily a closed-form nonlinear equation of the direct kinematics and use not the Newton-Raphson method, but the Secant method to obtain quickly the solution from ...

• Journal of the Korean Society for Precision Engineering
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• v.29 no.1
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• pp.64-71
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• 2012

In this paper, a parallel manipulator is comprised of two sliders and four links. Sliders execute a linear reciprocating motion depending on parallel guides and make the connected links rotate. A couple of links connected by sliders do coupling motion. The end-effector called a link tip has orientation angle. Through the kinematics analysis of this manipulator, we found displacement, velocity and acceleration using direct and inverse kinematics. We used equations that derived from this analysis and determined five constraint conditions. These conditions had much to do with rotation states of links, the relative relation of link length and coupling motion state. To verify those, we suggest a new algorithm regarding constraint conditions of a manipulator. With the result which performed the algorithm, we found out that operation range of coupled links was limited by relative relation of link length and that manipulator was not able to carry out a series of link motion, in case of being the link vertical between two parallel guides.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.580-583
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• 2002

This paper presents a novel pose description corresponding to the structure characteristics of parallel manipulators, which is convenient and intuitionistic to us. A class of 3-RSR parallel manipulator is considered here. Through analysis on geometry theory, we obtain a new method of the closed-form solution to the forward kinematics. The closed-form solution contains two different meanings-analytical and real-time. So we reach the goal of practical application and control. A numerical example is also presented and are verified by an inverse kinematics analysis. It shows that the method has a practical value for real-time control.

• Korean Journal of Computational Design and Engineering
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• v.13 no.2
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• pp.153-161
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• 2008

This paper proposes an efficient algorithm for deriving inverse kinematics equation of 5-axis machine. Because the joint order and direction of 5-axis machine are different for each type of machine, each type of machine needs its own inverse kinematics equation for post-processing of NC data. Also derived inverse kinematics equation may cause problems of indeterminate and inconsistent solution. In order to resolve these problems, we have developed a generic method to derive direct kinematics equation by considering orthogonal joints of 5-axis machines. Using this method, we also have proposed a general algorithm for deriving inverse kinematics equation for various types of 5-axis machines.