Simple machines can be regarded as the elementary "building blocks" of which all more complicated machines (sometimes called "compound machines"[6][7]) are composed.[2][8] For example, wheels, levers, and pulleys are all used in the mechanism of a bicycle.[9][10] The mechanical advantage of a compound machine is just the product of the mechanical advantages of the simple machines of which it is composed.
A compound machine is a machine formed from a set of simple machines connected in series with the output force of one providing the input force to the next. For example, a bench vise consists of a lever (the vise's handle) in series with a screw, and a simple gear train consists of a number of gears (wheels and axles) connected in series.
compound wheel and axle physics pdf 23
Simple machines are elementary examples of kinematic chains that are used to model mechanical systems ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a kinematic pair called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of the kinematic pair called a sliding joint. The screw is usually identified as its own kinematic pair called a helical joint.
However, a more successful strategy was identified by Franz Reuleaux, who collected and studied over 800 elementary machines. He realized that a lever, pulley, and wheel and axle are in essence the same device: a body rotating about a hinge. Similarly, an inclined plane, wedge, and screw are a block sliding on a flat surface.[32]
In the earlier studies concerning compound bow models, the pulleys at the tips of the limbs are either similar systems both consisting of two round eccentrics [2], similar systems both consisting of one round wheel and one non-round cam [3], or there is one round wheel at the other tip of the limb and the system of three non-round cams at the other [4, 5]. In the models including non-round cams, the cams are approximated as components with mixed properties of a circle and a changing lever at the same time, in order to simplify the admittedly complex system of the compound bow. However, in the viewpoint of cam design, a more detailed treatment of cams is needed.
Let us consider a compound bow with similar cam systems at the tips of the limbs. Let us assume that the bow is symmetric with some vertical line, which is also the line in which the arrow moves when the bow string is drawn or released from the center of the string; the reader is noted that this is not always the case for real twin-cam bows. We further assume that the bow is in a horizontal position so that the grip and riser are above the cables and the string, and the line between the axle points of the cams is horizontal, as in Fig. 1.
The model was first tested by using the parameters of the round-wheel compound bow measured in [2]. The string and the cable cam radius were gained by cubic spline interpolation of the polar transformations of the known eccentrics of paper [2]. The first and the second derivatives of the cubic spline are also continuous, which is an important minimum requirement for the displacement diagrams of the high-speed cam systems [9].
Bending your Pinewood Derby car axles with a bending tool will make the wheels ride up against the nailhead, which creates less friction than if the wheel is bouncing around and rubbing against the wooden Pinewood Derby car body. See video above for details. 2ff7e9595c
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