Variable Spherical Solid

Solid sphere with variable dimensions and mass properties

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Libraries:
Simscape / Multibody / Body Elements / Variable Mass

Description

The Variable Spherical Solid block models a solid sphere whose dimensions and mass properties can change during simulation. The block uses the scalar equation

$$m=\rho *\frac{4}{3}*\pi *r^3,$$

where:

• m is the mass of the solid sphere.

• ⍴ is the density of the solid sphere.

• r is the radius of the solid sphere.

You can compute any variable by providing the other two variables. If the equation is rearranged and any variable appears in the denominator, ensure that this variable is nonzero to maintain the validity of the equation. Also, when calculating the radius of the solid sphere, mass and density must share the same sign.

To model a variable solid sphere, select one parameter to compute automatically, then define the remaining parameters by using either constant values or time-varying physical signals. The reference frame is located at the center of the solid sphere.

Examples

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.

• Open Model

Ports

Frame

R — Reference frame

frame

Reference frame of the variable solid sphere, fixed at the center of the sphere.

Input

r — Radius

physical signal

Radius of the variable solid sphere. The value must be nonnegative.

Parameter Dependencies

To enable this port:

• Do not set Automatically Compute to Radius.

• Under Geometry and Inertia, set the Radius parameter to Provided by Input.

rho — Density

physical signal

Density of the variable solid sphere.

Parameter Dependencies

To enable this port:

• Do not set Automatically Compute to Density.

• Under Geometry and Inertia, set the Density parameter to Provided by Input.

m — Mass

physical signal

Mass of the variable solid sphere.

Parameter Dependencies

To enable this port:

• Do not set Automatically Compute to Mass.

• Under Geometry and Inertia, set the Mass parameter to Provided by Input.

Output

r — Radius, m

physical signal

Radius of the variable solid sphere.

Parameter Dependencies

To enable this port, under Sensing, select Radius.

rho — Density, kg/m^3

physical signal

Density of the variable solid sphere.

Parameter Dependencies

To enable this port, under Sensing, select Density.

m — Mass, kg

physical signal

Mass of the variable solid sphere.

Parameter Dependencies

To enable this port, under Sensing, select Mass.

com — Center of mass, m

physical signal

Center of mass of the variable solid sphere. The signal is a 3-by-1 vector that contains the Cartesian coordinates of the center of mass, expressed in the reference frame of the variable solid sphere.

Parameter Dependencies

To enable this port, under Sensing, select Center of Mass.

I — Inertia matrix, kg*m^2

physical signal

Inertia matrix of the variable solid sphere. The signal is a 3-by-3 matrix, expressed in the reference frame of the variable solid sphere.

Parameter Dependencies

To enable this port, under Sensing, select Inertia Matrix.

Parameters

Geometry and Inertia

Automatically Compute — Property to compute

Radius (default) | Mass | Density

Specify which variable of the solid sphere that the block calculates based on the values of the other variable.

Radius — Radius

Constant (default) | Provided by Input

Radius of the variable solid sphere. To use a fixed value, select Constant. To specify a time-varying value via a physical signal, select Provided by Input.

Parameter Dependencies

To enable this parameter, do not set Automatically Compute to Radius.

Value — Value of radius

1 m (default) | nonnegative scalar

Radius of the variable solid sphere. The radius remains constant throughout the simulation.

Parameter Dependencies

To enable this parameter:

• Do not set Automatically Compute to Radius.

• Under Geometry and Inertia, set Radius to Constant.

Density — Mass per unit volume of material

Constant (default) | Provided by Input

Mass per unit volume of the material. To use a fixed value, select Constant. To specify a time-varying value via a physical signal, select Provided by Input.

Parameter Dependencies

To enable this parameter, do not set Automatically Compute to Density.

Value — Value of density

1000 kg/m^3 (default) | scalar

Density of the variable solid sphere. The value remains constant throughout the simulation. To model the effect of a void or cavity in a compound body, use a negative value. The overall mass of the compound body must remain positive.

Parameter Dependencies

To enable this parameter:

• Do not set Automatically Compute to Density.

• Under Geometry and Inertia, set Density to Constant.

Mass — Mass

Provided by Input (default) | Constant

Mass of the variable solid sphere. To use a fixed value, select Constant. To specify a time-varying value via a physical signal, select Provided by Input.

Parameter Dependencies

To enable this parameter, do not set Automatically Compute to Mass.

Value — Value of mass

1 kg (default) | scalar

Mass of the variable solid sphere. The value remains constant throughout the simulation. To model the effect of a void or cavity in a compound body, use a negative value. The overall mass of the compound body must remain positive.

Parameter Dependencies

To enable this parameter:

• Do not set Automatically Compute to Mass.

• Under Geometry and Inertia, set Mass to Constant.

Graphic

Type — Graphic to use for visualization

From Geometry (default) | Marker | None

Type of the visual representation of the solid, specified as From Geometry, Marker, or None. Set the parameter to From Geometry to show the visual representation of the solid. Set the parameter to Marker to represent the solid as a marker. Set the parameter to None to hide the solid in the model visualization.

Visual Properties — Parameterizations for color and opacity

Simple (default) | Advanced

Parameterizations for specifying visual properties. Select Simple to specify Diffuse Color and Opacity. Select Advanced to specify more visual properties, such as Specular Color, Ambient Color, Emissive Color, and Shininess.

Dependencies

To enable this parameter, set Type to From Geometry or Marker.

Shape — Shape of marker to represent to the solid

Sphere (default) | Cube | Frame

Shape of the marker by means of which to visualize the solid. The motion of the marker reflects the motion of the solid itself.

Dependencies

To enable this parameter, set Type to Marker.

Size — Width of the marker in pixels

10 pixels (default) | scalar

Width of the marker in pixels. This width does not scale with zoom level. Note that the apparent size of the marker depends partly on screen resolution, with higher resolutions packing more pixels per unit length, and therefore producing smaller icons.

Dependencies

To enable this parameter, set Type to Marker.

Diffuse Color — Color of light due to diffuse reflection

[0.5 0.5 0.5] (default) | 3-by-1 or 1-by-3 vector with values in the range of 0 to 1 | 4-by-1 or 1-by-4 vector with values in the range of 0 to 1

Color of the light due to diffuse reflection, specified as an [R,G,B] or [R,G,B,A] vector with values in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

The diffuse color reflects the main color of the rendered solid and provides shading that gives the rendered object a three-dimensional appearance.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Opacity — Graphic opacity

1.0 (default) | scalar in the range of 0 to 1

Graphic opacity, specified as a scalar in the range of 0 to 1. A scalar of 0 corresponds to completely transparent, and a scalar of 1 corresponds to completely opaque.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Simple.

Specular Color — Color of light due to specular reflection

[0.5 0.5 0.5 1.0] (default) | 3-by-1 or 1-by-3 vector with values in the range of 0 to 1 | 4-by-1 or 1-by-4 vector with values in the range of 0 to 1

Color of the light due to specular reflection, specified as an [R,G,B] or [R,G,B,A] vector with values in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1. This parameter changes the color of the specular highlight, which is the bright spot on the rendered solid due to the reflection of the light from the light source.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Ambient Color — Color of ambient light

[0.15 0.15 0.15 1.0] (default) | 3-by-1 or 1-by-3 vector with values in the range of 0 to 1 | 4-by-1 or 1-by-4 vector with values in the range of 0 to 1

Color of the ambient light, specified as an [R,G,B] or [R,G,B,A] vector with values in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

Ambient light refers to a general level of illumination that does not come directly from a light source. The Ambient light consists of light that has been reflected and re-reflected so many times that it is no longer coming from any particular direction. You can adjust this parameter to change the shadow color of the rendered solid.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Emissive Color — Self-illumination color

[0.0 0.0 0.0 1.0] (default) | 3-by-1 or 1-by-3 vector with values in the range of 0 to 1

Color due to self illumination, specified as an [R,G,B] or [R,G,B,A] vector in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

The emission color is color that does not come from any external source, and therefore seems to be emitted by the solid itself. When a solid has an emissive color, the solid can be seen even if there is no external light source.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Shininess — Highlight sharpness

75 (default) | scalar with value constrained to 0–128

Sharpness of specular light reflections, specified as a scalar number on a 0–128 scale. Increase the shininess value for smaller but sharper highlights. Decrease the value for larger but smoother highlights.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Extended Capabilities

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

Version History

Introduced in R2017b