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Kinematics model of hexapod. Part 1. Matix models

Keywords:

V.Kh. Ankudinov – Post-graduate Student, Department «Computer systems and networks», Kaluga branch of the Bauman MSTU E-mail: vladislav.ankudinov@gmail.com A.V. Maksimov – Ph. D. (Eng.), Associate Professor, Department «Computer systems and networks», Kaluga branch of the Bauman MSTU E-mail: av_maximov@bk.ru


Hexapod – a six-legged walking robot. Due to the fact that for the static stability of the robot only three legs are needed, hexapods have high stability and maneuverability. Hexapods thus are promising robots for research, capable of working in dangerous areas otherwise inaccessible for humans, such as repairs to the engine rooms of ships, pipes, removing debris, or space exploration. For the synthesis of the statically stable gait of the robot, it\'s necessary to solve the problem of inverse kinematics. To do so, one must first solve the forward kinematics problem, namely, to find the coordinates of the ends of the robot legs with given values for the joint angles. To solve the problem of forward kinematics, a kinematic scheme should be described. There are many kinematic schemes for hexapods. The most widely used among researchers is an insect like scheme with three degrees of freedom for each leg: one for the horizontal plane and two for the vertical. This arrangement combines simplicity and flexibility, that is to say that three – is the minimum necessary number of degrees of freedom to allow the arbitrary specifications of foot end coordinates. Kinematic schemes of hexapods are also divided according to the method of leg placement: symmetrical in the longitudinal plane, or axisymmetric, each of which has its own advantages and disadvantages. The Hexapod design «Snejinka» has an axis of symmetry and has a number of features associated with the desire to reduce the load on the servos and make the design more compact, which led to the placement of two of the three servos for each leg in the coxa. A more compact design causes the coxa-femur hinge to be displaced not only along the axis X but also along Y and Z. Thus the generic hexapod kinematic scheme, that allows for specifying hinge displacements in many axis was introduced. It was shown that generalized kinematics scheme can be easily reduced to different simplified schemes, thus, methods developed from the example of axisymmetric hexapod «Snejinka» using generalized kinematic scheme applicable to the broader class of hexapods, namely to all insect like hexapods with three degrees of freedom for each leg, wherein the first coupling hinge rotates in the horizontal plane, and the second and third in the vertical (twisting of joints along the X axis are absent, the place of contact with the ground is considered to be a point at the end of the leg and the position of this point at the leg is considered to be the same. In the first part of the article for the described kinematic scheme, the solution for the forward kinematics problem using homogeneous matrices is presented. The results can be used to further solve the inverse kinematics problem in different ways.
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