Inverse Kinematics and Velocity Analysis of a 6-DOF Hexapod-Type Manipulator with a Circular Guide

Fomin, Alexey; Антонов, А. В.; Petelin, Daniil; Glazunov, Victor; Ceccarelli, Marco

doi:10.1007/978-3-030-75271-2_2

Cited by 1 publication

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“…Next, we check the leg interference for each point in fp P g. To find vectors b s i and p Ai , used in equations ( 11) and ( 12), we apply the inverse kinematics algorithm. 17,18 Geometrically, we should find points where a sphere, centered in B i with radius L, intersects a circular guide. We know this intersection will occur because we check points from fp P g that already satisfy constraints 1-3.…”

Section: Numerical Algorithmmentioning

confidence: 99%

“…Table 1 enumerates the geometrical parameters and constraint values corresponding to the CAD model and previous works. 17,18 We do not specify the value of l and how to calculate OC i in equation ( 14) because our algorithm does not need these parameters.…”

Section: Examplesmentioning

confidence: 99%

“…In this subsection, we will use normalized Jacobian matrix J n , calculated using equations (19) or (20), to compute conditioning index (18) over the workspaces, determined in previous sections and presented in Figures 6 and 7. We will apply the same notation k �1 , keeping in mind that we use normalized matrix J n .…”

Section: Examplesmentioning

confidence: 99%

“…In Ref. 18, we have found an expression that connects driving velocities _ q of the cranks and platform twist V P with respect to point P…”

mentioning

confidence: 99%

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Workspace and performance analysis of a 6-DOF hexapod-type manipulator with a circular guide

Антонов

Fomin

Glazunov

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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The present paper considers workspace and performance analysis of a six degree-of-freedom hexapod-type parallel manipulator with a circular guide. Compared to other similar manipulators, the design of this one allows locating all the drives fixed on the base and avoiding collisions between the carriages. The first half of the paper focuses on a procedure to determine the constant orientation (translation) workspace. The study first considers all the constraints that can affect the working area: constraints in active and passive joints, leg interference, and singularities. Next, the paper discusses the numerical procedure to construct the workspace. The proposed innovative approach combines the features of conventional geometrical and discretization methods. The suggested techniques are implemented in a MATLAB package and verified by examples with various orientations of the mechanism output link. The paper also discusses the accuracy of developed methods and mentions the required computational efforts. The second half of the work analyzes manipulator performance by calculating the conditioning index over the workspaces obtained earlier. The paper evaluates the conditioning index for an ordinary Jacobian matrix and a normalized one. In the latter case, two normalization approaches are considered: using a characteristic length and using linear velocities of three points selected on the mechanism output link.

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Section: Numerical Algorithmmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%