Kinematics of Linkages

Chapter 1

Abstract

tenon and time.

1. Introduction

coordinate system, see Figure 1.

2. The basic components

2.1 Tenon

3

Stanislav Barton

Optimization of Kinematics of

Keywords: mathematical modeling in Maple, transformation matrix,

angular velocity, angular acceleration, optimization

The inclined swinging pin simply transforms the rotary motion into a rotational oscillation. It consists of three components, a rotating inclined tenon, a crossbeam, and a stirrup. The pitch angle of the inclined tenon relative to the x-axis of its rotation is decisive for the kinematics of this joint. Too small inclination angle will result in small amplitude of oscillation; too much inclination will lead to an impulse dynamic stress that can damage the pin. The optimal angle of inclination can be determined from the mathematical model, created in the Maple environment, which uses linear algebra resources to describe the behavior of the joint. Vectors of coordinates of the critical points are created for each joint component. Furthermore, transformation matrices are created which describe the behavior of the corresponding kinematic chain in relation to the inclination angle of the inclined

The inclined swinging pin is used for the simple conversion of rotational motion into oscillation in many agricultural machines. For example, in combine harvesters, it is used to drive a mowing bar that cuts stems. It is composed of three basic components: an inclined tenon—red, a crossbeam—green, and a stirrup—blue, see Figure 1. We study the movement of individual components in a rectangular

Similar mechanisms are described, for example, in the book [1] that is available in an electronic version [2]. Many animations can be found on the Web, if you use keywords rotation to oscillation mechanism, Google will offer you over 20,000 links.

The pin is a basic component. Its basic part is an oblique nose. Its axis of symmetry forms an angle ϕ with the axis of rotation of the whole pin, which is identical to the axis x of the coordinate system. The axis of symmetry of the nose

Inclined Swinging Pin

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