Mass With Length (PB)

Mass with length and gravitational effects

Since R2024b

Libraries:
Simscape / Foundation Library / Translational / Elements

Description

The Mass With Length (PB) block represents a mass with length and gravitational effects that moves along an inclined rail. Gravity can induce motion along the rail.

The Mass With Length (PB) block is essentially a structural component that consists of a Mass (PB) block connected to a Spacer (PB) block.

Mass with length schematic

The force flow equations are:

$f_{a c c} = m \cdot \dot{v}$

$f_{a c c} = f + f_{g p}$

$f_{g p} = - m \cdot g \cdot \sin (θ)$

$l e n g t h = x_{F} - x_{B}$

$x_{L o g} = x_{B} + f r a c t i o n_{L o g} \cdot l e n g t h$

where:

f_acc is force proportional to mass acceleration. Positive force accelerates the mass in the positive direction.
f is net force of other mechanical components in the network acting on the mass.
f_gp is force proportional to the parallel component of gravitational acceleration, that is, to gravitational acceleration acting along the rail.
m is the mass.
v is the mass velocity. Ports B and F have the same velocity, v_B = v_F.
g is the gravitational acceleration.
θ is the rail incline angle.
length is the mass length.
x_B and x_F are the absolute positions of ports B and F, respectively.
x_Log is the absolute position of an intermediate point, if you enable the Log the position of an intermediate point option.
fraction_Log is the intermediate point fractional length from port B.

For example, to log the position of the center of mass, select the Log the position of an intermediate point check box and set the Intermediate point fractional length from B parameter to 0.5.

The Mechanical Translational Properties (PB) block specifies the gravitational acceleration and rail incline angle in the network. For more information, see Interpreting Logged Forces in Mass Blocks.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Examples

Gravity and Friction in the Position-Based Translational Domain

Configure gravity and gravity-induced friction effects in a position-based mechanical translational network.

Open Live Script

Ports

Conserving

expand all

B — Base port
position-based mechanical translational

Position-based mechanical translational conserving port that represents the base connection.

F — Follower port
position-based mechanical translational

Position-based mechanical translational conserving port that represents the follower connection. For nonzero length, port F has a more positive position than port B.

Parameters

expand all

Mass — Constant mass
`1 kg` (default) | positive scalar

Mass value. The mass is constant during simulation.

Length — Length of mass
`0 m` (default) | nonnegative scalar

Length of mass, that is, distance between ports B and F. This distance is constant during simulation.

Log the position of an intermediate point — Whether to log position of intermediate point
`off` (default) | `on`

Select this check box to log the position of an intermediate point between ports B and F, for example, of the center of the mass. For more information, see Data Logging.

Intermediate point fractional length from B — Fractional length of logged point from port B
`0.5` (default) | unitless scalar between 0 and 1

Fractional distance between port B and the intermediate point being logged.

Dependencies

To enable this parameter, select the Log the position of an intermediate point check box.

Extended Capabilities

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

Version History

Introduced in R2024b

Mass With Length (PB)