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Belt-Cable Spool

Source and sink of cord in a pulley system

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  • Belt-Cable Spool block

Libraries:
Simscape / Multibody / Belts and Cables

Description

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.

Examples

Block and Tackle with Four Pulleys

Block and Tackle with Four Pulleys

Models a block and tackle with four pulleys. Torque is applied to a winch which acts through the pulley mechanism to lift a load. Blocks from the Simscape™ Multibody™ Belts and Cables library are used to model the block and tackle.

Cable-Driven Cross Slide Table

Cable-Driven Cross Slide Table

Models an XY cross positioning table that uses a cable-driven mechanism. A single cable wraps around seven different pulleys and converts the rotational angle of the two input pulleys to the x-y position of the table.

Cable Robot

Cable Robot

Models a cable robot. The robot comprises 8 independent belt-cable circuits which control the 6 degrees-of-freedom of the mover. A ball is dropped from a fixed height down the center axis of the mechanism. The mover initially starts directly below the ball and the contact is modeled between the mover and the ball such that the ball bounces elastically when striking the mover. The objective of the mover is to perform increasingly complex maneuvers between successive bounces of the ball. The mover is motion actuated from which the necessary cable, pulley, and motor spool kinematics are computed.

Pulley Mechanism Right Angle Drive

Pulley Mechanism Right Angle Drive

Models a pulley mechanism that takes a torque applied to a winch and transmits it to a pulley rotated at 90 degrees to that winch. This example uses blocks from the Simscape Multibody Belts and Cables library to model a pulley mechanism that is not all in a single plane.

Cable Driven Space Manipulator

Cable Driven Space Manipulator

Models a cable driven space manipulator. The manipulator comprises of 2 links connected via a system of revolute joints. Each link consists of belt-cable circuits which drive the movements of the manipulator. It also consists of a spring-damper system which provides different stiffness requirements. A space application is shown in this example where the objective of the manipulators is to capture a small satellite. The manipulators start from folded states and then perform necessary maneuvers to extend and reach the desired position. The pulleys are motion actuated from which necessary belt-cable kinematics are computed.

Tower Crane with Trolley and Hoist

Tower Crane with Trolley and Hoist

Models a tower crane with a trolley and a hoist. The hoist can raise and lower a load, and the trolley moves the load towards and away from the tower. Blocks from the belts and cables library are used to model the pulleys that control lifting the load and moving the trolley.

Elevator

Elevator

Models an elevator system in Simscape™ Multibody™. The system is comprised of belt-cable pulley circuits which control the movement of the elevator and the door mechanism. The cable is approximated to be extensible by using high stiffness springs between the belt cable ends and the elevator. The motor pulley is motion actuated based on the necessary elevator kinematics computed from the Floor Number inputs. Effects of people entering and leaving the elevator are modeled using general variable mass blocks.

Forklift

Forklift

Models a forklift which uses the hydraulic and pulley mechanisms to perform the lift action. The tilting of masts is also controlled by hydraulic cylinders. The forklift comprises of 3 masts, namely main mast, top mast and fork mast. The main mast is connected to the chassis by revolute joints and its tilting is governed by the hydraulic tilt cylinders. The top mast slides over the main mast and its motion is governed by the hydraulic lift cylinders. The fork mast slides on the top mast and hangs through belt-cable circuits which drives the movement of the fork mast. A common warehouse application is shown in this example where the objective of the forklift is to grab a box, pass over a bump and place the box in the racks. Spatial Contact Force blocks are used at all contact locations to model the contact between the bodies. The contact between the ground surface and the wheels are modeled using infinite plane block and the contact between the forks and the box are modeled using the point blocks.

Ports

Frame

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Reference frame for attachment of the spool to the remainder of a multibody model.

Belt-Cable

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Point of tangency between the center line of the cord and pitch circle of the spool.

Parameters

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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.

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: Unrestricted.

    Use port qfa for this measurement.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2018a

See Also

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