Source and sink of cord in a pulley system
Simscape / Multibody / Belts and Cables
The Belt-Cable Spool block represents a cylindrical drum on which to wind (and from which to unwind) the cord of a pulley system. The spool marks an end to the cord and the point at which a motor or other power source often pulls on a load. A Belt-Cable End block generally marks the second tip of the cord, to which the load itself is commonly attached. Depending on whether it is winding or unwinding, the spool can behave as an infinite source of cord or as an infinite sink of the same.
The spool serves as an interface between the belt-cable domain specific to pulley systems and the frame domain general to all other multibody components. The belt-cable port (A) identifies the tip of the cord to be wound on the spool and the relative placement of that tip within a pulley system. A frame port (R) identifies the reference frame of the spool and its placement in the broader multibody model.
The degrees of freedom of the spool are a function of the joint by which the spool connects to other components. It is common for a revolute joint to provide those degrees of freedom; they reduce in this case to rotation about a single axis (that of the spool). Actuation inputs, specified directly through the joint by means of torque or motion signals, serve to drive the spool and to wind (or unwind) the cord.
The cord enters and exits the drum in tangency with the drum circumference. Consistent with the right-hand rule, the winding is in a counterclockwise direction about the rotation axis of the drum. This axis is by definition the z-axis of the local reference frame (R). To reverse the direction of the winding, you must flip the local reference frame so that the z-axis points in the opposite direction—for example, by the application of a frame rotation through a Rigid Transform block.
The surface of the spool (smooth or grooved) is not considered in the model. In addition, the cord is assumed to wrap around the spool in a circle that is of constant radius (that of the pitch circle) and coplanar with the transverse cross section of the winch. Changes in spool radius due to winding are ignored.
By default, the cord can enter and exit a spool at an angle to its center plane (θ in the figure). This angle can vary during simulation—for example, due to translation of the spool on a prismatic joint. While the contact point is always in the center plane of the spool, the spool can move when mounted on a joint. The cord can also be constrained to enter and exit the spool in its center plane. Whether this constraint is enforced depends on the settings of the Belt-Cable Properties block.
The inertia of the spool and of the cord wound on it are also ignored. To capture the inertia of a spool of fixed mass, use the Cylindrical Solid or Inertia block. Consider the Cylindrical Solid block if solid geometry is important in the model. To capture the variable mass properties of a cord as it winds on, and unwinds from, the spool, use a block from the Variable Solids library—for example Variable Cylindrical Solid or General Variable Mass.
R— Local reference frame
Reference frame for attachment of the spool to the remainder of a multibody model.
A— Spool cable attachment point
Point of tangency between the center line of the cord and pitch circle of the spool.
Pitch Radius— Distance from the center of the spool to the center line of the cord
10 cm(default) | positive scalar in units of length
Distance from the center of the spool to the running axis of the cord measured in the arc within which contact occurs. In compound pulley systems, the differences in pitch radii often determine the ratio at which speed is reduced or torque is augmented.
Sensing— Selection of kinematic variables to sense
Unchecked(default) | Checked
Selection of kinematic variables to sense. Select a check box to expose a physical signal port for the corresponding variable. The variables available for sensing are:
Spool Angle A — Angle, measured in the xy plane of the reference frame, from the local x-axis to the line between the frame origin and point of contact A.
If the point of contact is above the xz-plane (in the +y-region of the reference frame), the angle is positive. If the point of contact is below the xz-plane, the angle is negative. The angle is zero when the point of contact happens to be exactly in the xz-plane.
The angle is not modular. Rather than be constrained to a 360-degree range—snapping back to the beginning of the range after completing a turn—the measured value changes continuously with repeated turns. Every turn that the drum makes adds (or subtracts) 2π to the measurement.
Use port qpa for this measurement.
Fleet Angle A — Angle from the xy-plane of the reference frame to the cord at point of contact A. The xy-plane is the same as the center plane of the drum.
If the cord approaches the point of contact from above the xy-plane (in the +z region of the reference frame), the angle is positive. If the cord approaches from below, the angle is negative. The angle is zero when the cord approaches the point of contact in the center plane of the drum.
The angle is modular, which is to say that its value is bound—here, between -π/2 to +π/2. This range is open. The measured value can vary between -π/2 and +π/2, but it cannot hit either limit.
Note that if the Drum Belt-Cable
Alignment parameter of the Belt-Cable Properties block is set to
Monitored Planar, the pulley
assembly is required to be planar, and the fleet angle is
therefore always zero. To model a nonplanar assembly, use the
default setting for that parameter:
Use port qfa for this measurement.