# Spherical

Primitive joint with three rotational degrees of freedom

## Library

First Generation/Joints

## Description

### Warning

This content is specific to Simscape™ Multibody™ First Generation software. First-generation features are slated to be deprecated and should be avoided.

The Spherical block represents three rotational degrees of freedom (DoFs) at a single pivot point, a "ball-in-socket" joint. Two rotational DoFs specify a directional axis, and a third rotational DoF specifies rotation about that directional axis. The sense of each rotational DoF is defined by the right-hand rule, and the three rotations together form a right-handed system. A spherical joint is one of the Simscape Multibody primitive joints, along with prismatic and revolute.

You cannot connect an Actuator to a Spherical. Unlike the Gimbal block, the Spherical block cannot become singular.

Spherical Motion of Follower (blue) Relative to Base (red)

### Satisfying Joint Requirements

A Joint block represents the relative degrees of freedom between two bodies, not the bodies themselves.

You must connect any Joint block to two and only two Body blocks, the base and the follower. All Joints have two connector ports for these connections, defining the direction of joint motion (base to follower). You connect each side of the Joint block to these Body blocks at a Body coordinate system (CS) port.

You specify the joint primitive axes, if any, in the Joint dialog.

#### Assembly Restrictions on Assembled Joints

This Joint block is assembled and places restrictions on the connected Body CSs.

• If the Joint has no prismatic primitives, the origins of the connected Body CSs on either side of the Joint must be spatially collocated points, to within assembly tolerances.

• If the Joint has one or more prismatic primitives, the origins of the connected Body CSs must lie in the span of the prismatic axes:

Number of Prismatic PrimitivesSpan of Primitive Axes
OneAlong the primitive axis
TwoIn the plane of the primitive axes
ThreeAnywhere in three-dimensional space

## Dialog Box and Parameters

The dialog has two active areas, Connection parameters and Parameters.

## Connection Parameters

The base (B)-follower (F) Body sequence determines the sense of positive motion. Positive rotation is the follower rotating in the right-hand sense as shown in the figure above.

Current base

When you connect the base (B) connector port on the Spherical block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Spherical Base and Follower Body Connector Ports.

Current follower

When you connect the follower (F) connector port on the Spherical block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Spherical Base and Follower Body Connector Ports.

Number of sensor/actuator ports

Using this spinner menu, you can set the number of extra connector ports needed for connecting Joint Sensor blocks to this Joint. The default is `0`. A Spherical cannot be connected to a Joint Actuator.

The motion of a Spherical is three DoFs specified in quaternion form.

Spherical Base and Follower Body Connector Ports

## Parameters

Switch between the Axes and Advanced tabs.

### Axes Tab

The entries on the Axes tab are automatic. They specify the orientation of the spherical DoF that the Spherical represents.

Name

This column automatically displays the name of each primitive joint contained in the Joint block. For Spherical, there is only one primitive joint, a spherical, labeled `S`.

Primitive

This column automatically displays the type of each primitive joint contained in the Joint block. For Spherical, there is only one primitive type, labeled `Spherical`.

Reference orientation [x y z]

This field is not active.

Reference CS

This field is not active.

The Advanced tab is optional. You use it to control the way Simscape Multibody simulation interprets the topology of your schematic diagram.

Mark as the preferred cut joint

In a closed loop, the simulation internally and automatically cuts one and only one joint.

If you want this particular joint to be weighted preferentially for cutting during the simulation, select the check box. The default is not selected.

See Modeling Degrees of Freedom for more on representing DoFs with Joints.

See Checking Model Topology and How Simscape Multibody Software Works for more on closed loops and cutting.